Okay, let's give it a shot. While the obvious picks like Metroid Prime 3, Xenoblade Chronicles, Zelda Skyward Sword, Wii Sports, Smash Bros Brawl, Fire Emblem Radiant Dawn, DKCR, The Last Story and Sin & Punishment Star Successor have been mentioned plentiful times already, I'd like to give a shout-out to some more niche titles that I enjoyed a lot like Final Fantasy Crystal Chronicles: The Crystal Bearers. It may not be as complex like mainline games, but I found the main story to be quite exciting and tense. The presentation values are not too shabby either. Gameplay wise it may just be a lot of waggling and pulling, but there are so many funny interactions that can emerge throughout the entire journey that made me really like this game.

Then there were some turn-off-your-brain-and-enjoy-the-ride like action games that hooked me a lot like No More Heroes 1+2, Disaster: Day of Crisis, Red Steel 1+2, The Conduit and both Resident Evil light gun games. 

I also want to mention SSX Blur, Super Paper Mario, Endless Ocean, Pandora's Tower, Trauma Center, Project Zero: Crimson Butterfly, Silent Hill: Shattered Memories, Cursed Mountain, Deadly Creatures, and Battalion Wars II. Not one of these games plays similarly to any other. The amount of variety is insane.

Finally, I will always have a soft spot for Metroid: Other M, not matter what others think. And last but not least, I conclude that Kirby's Epic Yarn might be the best Wii game because it is a joy ride from start to finish.

World of Goo was also great on the Wii. it was the only original digital only game I got for the system.
Spent a lot of hours trying to build the highest tower in that game, felt like a 3 year old kid discovering blocks, trying to reach the roof.

After Galaxy I would honestly say Resident Evil 4: Wii Edition. Still my favourite version of my fave Resident Evil game.

However if we are to exclude ports and go with exclusives my pick is Mario Strikers Charged! Absolutely love this game, it's one of a few titles I've actually gone to a tournament for and it was the only Wii title I played often online (I usually just prefer local play).

Thanks, that I am not the only one remembering the awesome Pandora's Tower.

Yes, I totally forgot Endless Ocean and Battalion Wars II. Definitve unique and fun experiences (although apparently there is a new Endless Ocean on Switch.

Deadly Creatures seriously messed with my sense of space in the spider sections. As you did run upside down or at the sides sometimes, and then also jump into another position I sometimes lost all sense for direction. Also it had a funny plot, with two majestic creatures having an important struggle of dominance, while in the background some silly humans are fighting over something pointless like money and ultimately are dying.

Same.

Good shout; the Project Zero/Fatal Frame 2 reimagining was one of my favourite games on the system and my GOTY for 2012. So brilliantly creepy and such a masterful slow burn of tension and atmosphere.

Such a shame it never got a North American release, it deserved to be more widely played.

The Legend of Zelda: Twilight Princess. I don't care if it's seen as a GameCube game. It's my number one. I see it as a Wii game lol :P.

This list took a VERY long time to write but I had fun writing it. I tried to describe my reasons below each title. Most of these Wii games in my list have extremely nice good box-art (Zelda's, Okami, Super Paper Mario, Red Steel 2, Kirby's Epic Yearn, Xenoblade Chronicles, etc), I forgot how nice they look. Mario Galaxy 1 & 2 look really nice too (but I'm not allowed to mention them in this thread lol) I was just looking through my game collection when writing this and it made me think of happy times and I got lost in the nostalgia.
Anyway here is my list-


The Legend of Zelda: Twilight Princess:
This may be my most hyped game of all time. The Wind Waker was my first Zelda Game I played. I loved it so much, then I bought the Zelda Collector's Edition on GameCube. I was a major Zelda fan by then. Zelda became my fav game franchise, then E3 2004 happened and I was blown away like everyone else when I saw the Twilight Princess trailer. The 2.5 years wait between E3 2004 and end of 2006 felt like a lifetime.
The graphics, gameplay, exploration, backtracking, figuring were/what to do next all made it super immersive. I love the environments a lot. The art style is timeless and also that version of Link is my fav version.
Also the semi open-world structure is the perfect mix between open and linear. It was figuring out what to do that made the backtracking metroidvania-esque world immersive. Also with it's day/night cycle and weather system, my time fishing in the cherry blossom part was immersive. I remember going into 1st person mode and focusing on the water, seeing the rain hitting the water and the cherry blossoms falling from the trees into the water. The leaves floating around was captivating and visually pretty. This was when open-world games were not overdone so this was a very special experience back then. Especially with the pretty graphics. True art is timeless.

Metroid Prime Trilogy:
I originally had all 3 (first to on GameCube, then the 3rd one on Wii), but I never got round to completing them until the Trilogy for the Wii. I bought it right at the end of the 7th gen and didn't get round to playing it until the Wii U came out.
I played this on Wii U as the Wii U was backwards compatible with Wii games including the Wiimotes. I played all 3 games in the trilogy back-to-back and loved it so much. The motion controls felt like VR without the headset. It felt amazing. The style and look of the game was so nostalgic and retro (mysterious dark sci-fi). I felt so immersed in the dark at night in my bedroom. This was an excellent moment in my life.
Scanning the environments for clues creates a mystery element which other games don't do. Looking for secrets and backtracking around the intricate labyrinth design was so immersive. This is a hybrid of genres - FPS, Action, Adventure, Openworld-ish, Metroidvania, Puzzle, Mystery, Sci-Fi, shooter, etc. The genres are used like how colours are in a colour-pallet of a professional artist, were every colour (genre) is used with careful precision to make the whole balance of the painting (game design) work which makes the overall art (game) timeless and unique. It not only stand out but shines as one of a kind. There is no game franchise like this.

Xenoblade Chronicles:
I also bought this just when the Wii U got released, so I played it on the Wii U as it is backwards compatible. When FF13 was a let-down and Tales of Vesperia was good but too similar to Tales of Symphonia, this game filled my JRPG needs and more. The story, exploration, environments and the sense of progression kept me playing until completing it. The environments are so pretty. The unique combat made it feel fresh and upgrading the weapons/armour/characters had so much layers of complexity to it I still learn all there was to learn even after becoming level 100 and completing it. It has insane graphics for the Wii. I loved this so much. This is a high-end JRPG that ALL JRPG fans should play. The characters, story and orchestrated music are so rememberable too.

Resident Evil 4:
The motion controls were the best. I didn't realise there was a more fun way to playing it than the GameCube controller (same with Metroid Trilogy). The graphics were still the best (or one of the best) on the Wii despite it being a GameCube title. I already had this on the GameCube but always wanted to play Ada's side of the story and finally got to play it when the additional content got ported over (as Ada's story was only PS2 and not GameCube).
Resident Evil is my fav game franchise (as well as Zelda and possibly Mario too) and have been playing Resi since the PS1 trilogy, and was super hyped when it was being released on the GameCube. So the Resi 4 Wii port naturally filled a hole when playing it with motion controls.

Red Steel 2:
This was like playing a VR game. The motion controls were perfect. It's a shame it got released near the end of the Wii's life cycle because it was that sword-slashing game everyone dreamt of when they first heard about the Wii. It's art style did so well for the Wii and the gameplay was super fun. I liked exploring the environments too. How you could use the sword as a gun and point it at the screen worked so well. Switching between the shooting mechanic and sword swinging was as simple and intuitive as doing it in real life. The combos that you would learn throughout the game made it even more fun the more you played it. The developers actually listened to the critics from Red Steel 1 and made a game that everyone wanted. I feel like the devs also wanted to make it too. I think they should definitely make a Red Steel 3 in VR. That will probably happen some day and would be amazing.

New Super Mario Bros Wii:
I loved the fun gameplay, colourful graphics & level-select overworld. The new items were so fun too and the red box looks amazing on my self in my game collection. This game felt (and still feels) special because of that red box.

Elebits/Eledees:
The gameplay was perfect with the motion controls. This is such an underrated gem on the Wii. It's immersive environment/story of being a kid alone in the house at night. Exploring the environment via motion controls was like a VR game before VR existed. So immersive.
Also the gameplay was really fun. It made me feel powerful being able to life any objects and rotate/throw them about. The physics were super fun.

Donkey Kong Country Returns:
The music to this game took me back in time to when I played DKC trilogy on the SNES. I had DKC3 and rented 1 & 2 (then bought them a couple of generations later). So when I heard the music I was in my happy zone. This was a happy time. The gameplay too was really fun and challenging at times. It's like Mario but for big boys lol. The nostalgia of DKC on the SNES made this game feel like magic to play. Its amazing.

Okami:
Back in the Wii era, the Wii couldn't run super-realistic HD games so Okami was the perfect port. Not only does it have the timeless and memorable art style. It's motion controls fit perfectly on the Wii. I wouldn't play this any other way (unless with a touch screen) to draw the symbols used for various actions. Also the characters are so like Zelda as well as the semi-open world approach to the metroidvania-eque game design. It is perfect for a Nintendo console. I loved the exploration and day/night and how that impacted the art style. Super immersive and rememberable.

Mario Kart Wii:
Fun Fun Fun. The tracks were amazing and visually captivating and really creative. This was my fav Mario Kart (as well as the DS version), until Mario Kart 8 got released. I never got round to playing Mario Kart 7 but some day I will pick it up to add it to my collection. This is why people bought the wheel, an accessory which felt so good. I sometimes preferred it without the wheel to feel the boost better when snaking around corners but sometimes liked the wheel too for a change to make it feel fresh. The online mode made this way more replayable than ever too.

Super Smash Bros Brawl:
The cutscenes were amazing. I remember thinking there's no way cutscenes could get any better than this. Although I did prefer the gameplay in Melee being more faster paced, but Brawl made up for it in its content such as character roaster, subspace embassy & additional items/weapons that would respawn in the matches. This would be the best multiplayer game around. Not only could I play it online but Solid Snake & Sonic was in the character roaster. I have a friend who always played Snake as MGS is his fav franchise of all time. This made the game so special in my friend group in my later teens.

The Legend of Zelda: Skyward Sword:
It may not be my fav Zelda game for it's linear approach. But it's linear approach did make the progression feel more rewarding than the two newest titles (BotW & TotK). I loved the motion controls even if everyone I know hated them lol. I really liked how Link's sword would mimic the hand gestures of the player even when the player isn't attacking. It made it feel really immersive. The storyline may be one of the best (if not, the best) in the Zelda franchise. The ending with Impa was an excellent twist as she dies of old age, yet it is the first game in the timeline. Because she is a time traveller, it was here I learned it was like a ghost of her in the other zelda games (but a living ghost) of her piecing through the timelines. She even had a younger self in Skyward Sword that added to the impact even more. The temples and boss fights were some of the most fun in the franchise too. The art style and characters had a lot of charm too.

Madworld:
As a teen, the blood, violence and swearing was like a protest against censorship in the entertainment industry. This grabbed my attention fast. I knew from a young age that violence in the media doesn't make people act violently in real life as human psychology is more complex than simple animals. This game was a middle finger to any clueless adults that generalise or think like Jack Thompson. It was highly self aware and super stylised in the black/white/red colour scheme. The commentary was full of humour and never failed to make me laugh. Each level felt different. It's story was similar to 'battle-royal' & 'The Running Man' (whatever that genre is called). The gameplay was fun and the repetitiveness never got old. You could use the environment to kill opponents in the must gory manner possible. The more blood, the more fun it was. It was rare to see something so edgy on the Wii, it was like a breath of fresh air.

Excite Truck:
Fun Fun Fun. The gameplay was were it was at. A super fast-paced racer where you make massive jumps over valleys by shaking the controller felt so good. Boasting while flying through the air and rotating the Wiimote to perform stunts (when successfully performed you would get another boast when landing on the ground). This was sooooo fun. You could also plug in an MP3 player to the Wii via USB and play any songs you wanted. I played a lot of Dragonforce as speed-metal was the perfect genre for such as fast paced game. It was like playing an action game in the guise of a racing game. I played this constantly for ages, the gameplay never got old as it was extremely fun and always miss the feel of playing it. The tracks utilised the gameplay mechanics so well too.

Kirby's Epic Yarn:
So adorable. I loved how you turn the Wiimote on its side and double tap left or right to change into the car. The art style is soooo cute :). It's my fav Kirby platformer of all time (and would be my fav Kirby game if Kirby Air Ride & Ghost Trap/Avalanche didn't exist). The secrets within the arty background and shiny gems felt collecting so special. UFO Kirby was so cute. I really loved this despite it being super easy. It was the charm that made this special. This game sits proudly on my shelf in my Wii collection as the box-art is really good too.

Super Paper Mario:
It has a lot of charm with it's art style. The characters and their stories made the experience more immersive making me want to progress more. It is a unique take on the Paper Mario franchise despite the fan-backlash of it not being turn-based or an RPG. I think it's a great puzzle game. The game design is so unique that FEZ was most likely inspired with the camera moving mechanic. I love the game box-art too. This is a unique gem that fans overlook (or pretend to). I still love Paper Mario: The One Thousand Year Door on GameCube, I never compare them as they are two completely different games that just use the same sub-series categorization of 'Paper Mario'. I think they are two great games of their own.

Wii Sports/Resort/Play/Fit/Warioware Wii:
I've condensed these down into one. We all had fun regardless of how hardcore we like to see ourselves as. The multiplayer features of the Wii series of games and their universally intuitive controls/design created so many experiences with our families. I played it in my living room with my family as a teen who would normally be introverted and in my bedroom otherwise, it made me know my own family members better so I have these games to thank for this. Whenever it was Christmas family would visit and we would all play Wii Sports & Warioware Wii in the front room. These memories cannot be replaced by anything.
I remember my Mom going through a faze of trying to loose weight (she still goes in/out of this faze to this day lol) and we would play Wii Fit. My Dad tried it once then quit after nearly falling over. We all had our game profiles and statistics. These games really brought the family together. Such good times.
I played a lot of pool with my friends in Wii Play. This was the perfect game for a casual get-together.
My personal fav is Wii Sports Resort as that was like Wii Sports but with way more content than any average casual game. The cycling was immersive and the sword fighting on the platform was so fun with the motion controls. These games created a lot of happy memories and I have to put these into my list.

Fragile Dreams:
This may not be considered a good game but it's atmosphere is so immersive. It's dark and creepy world has stuck with me till this day. It's an eerie world is full of ghosts and mystery. I loved the story and setting. It's more of an experience that you have to play to understand. The entire game is set in night time. There is a point in the game where you are outside and can see an Aurora in a starry sky. It's a very basic JRPG (if it can even be considered an RPG) and is such a different experience, it's hard to explain it feels like a gem in my collection. I love the art direction too.


P.S.
I always wanted to play Pandora's Tower & The Last Story but I never got round to buying them as they went up in price and I didn't have a job around 2012 and then 8th gen consoles got released. These would probably be in my list if I did get them.

Lord did I dislike that era for "core" Nintendo games. Motion controls+core Nintendo IP=a very unhappy me.

Having said that, the least-offensive title, for me, was Metroid Prime 3. There was also Xenoblade toward the end. It didn't really have motion controls but you still have to plug in the stupid add-on controller to play it semi-properly.

For me, that machine was great for casual gaming, like Wii Sports etc. That was where it excelled.

Wii Sports Resort

It's still the best motion controls game ever made.  I would love to see someone try to make a game that bests this title.  That would include picking one sport, like Archery, and making some awesome action adventure game with motion+ control archery as the main mechanic.  Even without this though, there is just so much endless fun in Wii Sports Resort.

I miss the Wii era so much. It was the last time gaming experiences felt fresh again, as I've been gaming for almost 40 years at this point. I'll divide this intro 3 tiers: 1. best overall 2. best multiplayer 3. best single experiences.

1. best overall is

I mean, ExciteBots was absolutely incredible. I don't know what kind of magic voodoo Monster Games put into it, but the gameplay is so absurdly refined that it still is one of the most impressive gaming experiences I've had in my life, online or off. The problem I saw for its commercial success (or lack thereof) is that I think it was released too close to MKWii (a game I completely skipped because of ExciteBots; no regrets). Unforgetable!

2. best multiplayer

I mean, my profile picture must show how much I love this one. Hunting in groups for more than a year was a blast. I purchased a WiiU pretty much just to play the enhanced version. No regrets either. Would do it again.

On the mjultiplayer side, there is one honorable mention to be presented:

FP Shooters never were the same to me after playing with a wiimote, as I stated in the other thread a few days ago. Superb.

3. best single player

I loved House of the Dead, enjoyed MadWorld, had a great time with Mercury Meltdown, but to this day I have an incredibly fond memory of No More Heroes. It's rough around some of the edges, but it's so crazy immersive you'll forgive some of the flaws. And nothing would beat finishing those combos felling like a fucking Jedi. And those Epic Boss fights? So much fun!

As you can see, I'm proud of the picks some of you guys made. Excellent taste!