The Legend of Zelda: Twilight Princess

Pretty unique games you won't find on other consoles:
Endless Ocean 2 (I've only played EO1, but people and reviewers say EO2 is even better)
Little King's Story
World of Goo (WiiWare; I expect it to be ported to PS3 this year)

If you like platformers (especially 2D) then buy Wario Land Shake. It's a very fun game that deserves more recognition than it got. Be sure to complete all missions.

I'd say Little King's Story and Rune Factory Frontier are niche titles you gotta have.

Also, excitebike World Rally from Wiiware.

I'd ask what kind of games you like before giving you any more recommendations, but I'll start with Red Steel 2, having finished it just yesterday.

It is surprisingly good, better than I expected actually as I think I had tempered my expectations somewhat due to some lukewarm reviews. It may not blow you away, I wouldn't quite call Nintendo quality but it is really good and it's major advantage is that it is quite unique.

The things I like about it include the very consistent and believable atmosphere, a great soundtrack which at times evoked memories of Firefly and some of the better graphics on the Wii running at a framerate that would make certain war shooters blush.

Having said that the story is kinda rubbish. Basically you are the sole member of the fabled Kusagari clan who has survived a brutal slaying by the new boss in town and having narrowly excaped with your life you have returned to claim vengeance and rid the town of the interlopers, and that about covers it.

You have the cliched but somehow still likeable sidekicks to help you on your way, teach you new moves, sell you new gear and provide the occasional pep talk but where the game excels is allowing you to feel like a total badass with a gun and a samurai sword.

This is achieved through some smart game design and the consistent, well implemented and very satisfying motion control and smooth and precise pointer control. It's not 1:1, it's not supposed to be but when you want to sidestep, slash and then shoot your hapless victim in the back of the head before he even knows what hit him, it happens everytime without a hitch. While your basic horizontal and vertical strikes in addition to stabs and basic gunplay are vital, it's the addition of various secret skills and finishers that add an extra layer of complexity and satisfaction to the controls as you always have options on how you want to dispose of the hords of oncoming flunkies. It does take a while to get used to the control, the game isn't 1:1 so it takes time to learn the games 'rules', but once you do it's gold.

So there it is. A very good game, the likes of which you can't play on any other system. Once you have played Mario Galaxy, Metroid Trilogy, Mario Kart and the other Wii must-haves do yourself a favour and buy or at least rent this little gem.

Rune Factory Frontier, Fire Emblem Radiant Dawn, RE 4: Wii, besides the games already listed. Get them.

Definately get Fire Emblem it is probably the most challenging and rewarding games on the Wii, with an awesome story.

@ blaydcor , awesome avatar Korgan is a serious bad-ass

I'd reccomend he get Fire Emblem: Path of Radiance before Radiant Dawn due to a couple factors:

1)Radiant dawn continues the story of Path of Radiance

2)Radiant Dawn is very tough. He needs the practice.

definitly grab new super mario bros wii and super mario galaxy 1 + 2.

Monster Hunter 3 if ur a fan and Wii Sports Resort is a really fun game as well.

Red Steel 2 is also a fun game that lets u use motion+