Trauma centre has you as a doctor, perfoming operations using the motion control or nunchuck. It is like something you have never played before i am pretty confident of that. Bully is really good on Wii. The motion control gestures work really well. I think there is something like 8 new missions over the ps2 version as well as new characters and 4 new lessons i believe. There is a lot of replay value after you have finished it. Little kings story is a must in my opinion. It's sort of like a RPG although it does seem quite childish as a lot of the enemies are like, giant chickens, turnips or clockwork knights. Again, i feel this will be unlike anything you have played before. Seems very original to me. Animal crossing is something completely different too if you have never played that before but i don't know if that would be your cup of tea. Plus, as you didn't have a gamecube you should try Chibi Robo NPC when it comes out. Yet again a totally unique experience. Am hoping the controls will work well. Wario ware is a totally bonkers game you could have fun with if you have friends round, as long as none of you minds making asses of yourselves!

I second the above.  World of Goo is great, one of my favourite Wii games.  You can try the PC demo if you like or just trust us and buy it.

Both trauma centers are a ton of fun and I've played both most the way through. I never got around to buying them though as there were always other games I wanted more.

The controls are perfect for the game. You use the joystick on the nunchuck to select what you want to use, and then the IR pointer and A/B buttons on the Wii Remote to use them. You have various situations (most of them totally unrealistic) and you show up and save the person from dieing at the last moment.

The game doesn't make sense too much of the time, because when you cut them open they are typically in fine physical shape just by looking at them, but when you get inside there is all sorts of crap going on. So you cut the guy open, and you find the entire remains of a shattered beer bottle and you wonder to yourself "how did that get in there with no outside cuts?"

So while strange and not making too much sense, you go off to fight mutant diseases and do all sorts of cool fast doctor stuff and the game is really challenging, but you can tone down the difficulty if you can't beat a stage.

That game will be too hard for little kids zack and wiki

Little king story is rated T that's not kid friendly

Pikmin is very hard for little kids. It'll make them break the controllers

All the games are ok. But becareful which you pick

Get pikmin New play control :)

Punch Out!! - Best game on the Wii for me anyways. It's great fun learning the Fighters patterns, it is an absolute must have!
Okami - The brush stoke on the wii makes it unique
Wario Land Shake It - Very good controls, and is great if you like Old School Mario style platformers

As far as Party games go:

M&S at the Olympic Games - Great variety of events, each has its own controls
Boom Blox - Lots a fun.  My wife likes this game and Wii Sports Tennis and that is all
Boom Blox Bash Party - See Boom Blox with add online play
Any Rabbids game your kids will LOVE THEM! - Funny Stuff it will make you laugh and is fun.  Gets repeditive though, but there are 3 to choose from now Rayman Raving Rabbids 1&2 and TV Party

I'll recommend a couple of games no one has mentioned yet:

Rayman Raving Rabbids - This is a mini-game compilation with lots of character and funny bits. It has rhythm based sections where you follow the beat of a song and get dancing bunnies as rewards of your success. It also has some on rails shooting. You shoot plungers at the rabbits so IMO that's not so violent for kids. It also has racing, jump the rope, cow toss, whack a mole (rabbit), and many more. It has a few frustrating mini-games, but the good ones outweigh the bad ones by a lot. The best thing about all this is that you can find this game really cheap almost anywhere. It's currently $15.49 at amazon and if you're ok with buying used games you could get it much cheaper.

Destroy All Humans: Big Willy Unleashed - This is a sandbox kind of game. You're an alien who has to accomplish some missions for your boss. You can go by foot shooting people with several weapons like the disintegrator, anal probes, bombs, and more. You can also ride the saucer and abduct people, destroy buildings and cause some mayhem. And in some missions you control a giant boy robot (Big Willy) and eat people, kill them with your gases and more. This game didn't get good reviews because it seemed like the reviewers liked the previous games more than this one and because it's not too long. I beat it in 10 hours, but I enjoyed every minute of it :). And just like the raving rabbids game, you can find this game for cheap too, I bought it for $15 brand new just to give it a try cause I had heard the other two were pretty good and was pleasantly surprised.

One more:
Mario Party 8 - This one is a collection of mini-games too, but you play on a board and roll dice to move like most board games. It also has good and bad mini-games. I borrowed it from a friend of mine to give it a try and my wife loved it. I guess it is lots of fun with kids too. The only bad thing, IMO is that this game is still very expensive. It still goes for $40 to $50 at most places and I've been waiting for it to be on sale or get a price drop, but like most nintendo titles it just doesn't happen.

Edit:

Damn it, PorkChopTD beat me to it with RRR

also, if u get (or have) a gc controller, get Paper Mario: The Thousand year Door
its an easy RPG so kids can play, but its fun for all ages. (my all time favorite game)

Right, before I tackle replies, I'll make a quick update where I am:

Enjoying it so far, although it looks terrible on my TV even at 480p. I'm getting over it slowly, but it's still somewhat of a barrier as the details are uber-fuzzy; the PS3 and PC have spoiled me, it seems -- I like 1080p.

I bought No More Heroes today as I saw it for very cheap, and bought a Gamecube controller at the same time. My wife reckons No More Heroes looks little better than a PSP game (and I'm inclined to agree), but it's a good bit of slashing fun, although most of my time is spent pressing 'A' tons and waggling the Wiimote about like crazy. Even though it seems repetitive, I'm intrigued enough to keep playing it at the moment. I also bought SNES Mario, as I loved the game as a kid (and was annoyed to see the emulation wasn't perfect).

Wii Fit is getting the most use just now, although I'm enjoying Galaxy as well. SSBB has yet to grab us, but that may change. The biggest surprise is that I've quite enjoyed the boxing in Wii Sports, although the controls are not precise at all. How are the controls on Punch-Out!! in comparison? The Golf game is just rubbish, but that's probably because I'm comparing it to Everybody's Golf, which is really good on PS3.

Lastly on this, now I have a Gamecube controller, what are everyone's recommendations for Wiiware and Virtual Console games (and Gamecube games, I suppose -- I never had a Gamecube, so, again, I'm a complete novice regarding its library)?

Thanks in advance.

There have been a few people recommending this now, and your description sounds awesome. I'll add that to the list, I think, although I'm not sure what I'm going to do regarding the pathetically small memory options on the machine.

Actually, on that, I have a question. If I delete a game from the Wii, will my saves be kept if I re-download the title later?

Right, out of those, Little King's Story sounds very intriguing. I'm looking for some RPGs. Anyone else recommend this?

And what is Animal Crossing?

Yes, I am that ignorant.