I have a "Nintendo" Wii; some of the games I own for it are:
Super Mario Galaxy- It's absolutely amazing. The graphics and gameplay are awesome!
Wii Sports- You get to play five sports games using the Wiimote: Tennis, Golf, Bowling, Baseball, and Boxing. You can get a lot of exercise with it and still have a lot of fun too.
Ben 10- If you like the cartoon, you'll probably love the game. I think you get to battle Vilgax at some point in the game.
Some of the games that I want for the "Nintendo" Wii are:
DragonBall Z: Budokai Tenkaichi 3- It has some of my favorite characters that you can play as, including Babidi, King Cold, and a lot of others. Also, you can use the Wiimote to recreate some of the characters' special attacks!
Pikmin 3- I loved the first two Pikmin games and this one is in development for the Wii. I hope it has a Pikmin Creator and an innovative new control system!
Super Smash Bros. Brawl- There are so many new characters for it, such as Diddy Kong, Captain Olimar from Pikmin, Pit/Kid Icarus, Sonic the Hedgehog, and so many others. The graphics are amazing and it's probably a lot of fun to play!
Pokemon Battle Revolution- I'm still a fan of the older Pokemon Stadium games, and this one lets you either use your own Pokemon from Diamond and Pearl, or use rental Pokemon to battle with.
Elebits- A game similar to Pikmin that lets you use the Wiimote to search for and catch electrical creatures named Elebits. I think it was one of the Wii launch titles.
Mario Super Sluggers- A baseball game involving Mario characters. You can play as Mario, Luigi, Yoshi, Bowser, and a lot of others; I think the Shy Guys are playable too! Also, you can use Mario-themed items, such as green and/or red Koopa shells, etc.