Here's the list of games I have for my Wii...followed by a list of games I have played on that I enjoyed:
I own:
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Animal Crossing: City Folk - I'm a fan of the Animal Crossing series. I think it's a good game but it can also get very addicting once you figure out which furniture you want to decorate your house with along with paying off your house rennovations.
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Cooking Mama: Cook Off - I'm also a fan of the Cooking Mama series...well...of Cooking Mama 2 for the DS and this one. There's another one out for the Wii as well but I haven't let myself get anymore games. ^^;; It's a cutesy cooking game. The recipes could very well be real recipes for each dish but the game's more meant to be cute than functional at cooking.
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Trauma Center: Second Opinion - Played my friend's copy for a little bit before I picked up my own. It can be hard/frustrating at times but as long as you're not squimish or faint at the sight of fake blood on the tv, this is a pretty good game.
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Harvest Moon: Tree of Tranquility - I'm a Harvest Moon fanatic! It's a farming simulation game that's cute and there's lots to do in order to make your farm successful. I haven't gotten very far in the game yet since I've discovered the Food Network and get distracted by random things around the apartment like cooking dinner and cleaning and other apartment things after I come home from work. I love it and I've been waiting for a very long time for this game to come out. This was actually why I waited to get a Wii. This was going to be the game that would force me to get a Wii. =P
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Guitar Hero: World Tour, Guitar Hero III: Legends of Rock, Guitar Hero: Aerosmith - If you like the Guitar Hero games, these are also fun and pretty convienient since you don't have to worry about cords anymore (except the one for the mic if you get World Tour). The drums for World Tour are pretty sturdy and I feel like I could pound on them and they wouldn't break.
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Nights - This is a game from the Sega Dreamcast. It's the same exact game...just for the Wii. I haven't personally played it yet but my brother did when I went home for Thanksgiving (my mom bought a Wii on a whim so I have access to a Wii wherever I go ^^;

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I think that's all the games I have so next list!
Friends owned and I played:
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Zelda: Twilight Princess - I played this for a little bit. It was easy to pick up for me since I had never played other Zelda games before this one (just don't play with immature college students around you -_-). I didn't play it more than once or twice since I was still in school and busy with applying for jobs and passing all my classes and getting a boyfriend. ^^;;
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Raving Rabbids (any) - Again, don't play this around immature college students. It's pretty fun and you'll get lots of good laughs from it. It might not be good for anyone younger than 12/13 if you're picky about some content (maybe?). But anyways...lots of laughing.
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Super Smash Brothers: Brawl - I personally don't like the SSB series but I have a lot of guy friends and they like to play so I have to deal sometimes. It's not because I'm usually lose, I don't mind that, it's the fact that a former friend that I played the GameCube version with was a sore-winner. Lots of content to try and unlock and you can definitely make each battle fun. But this is definitely more of a boys' game than a family game...unless your family likes that. =P
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Super Paper Mario for Wii - Not a bad game. If you've played the previous versions of Paper Mario, you'll probably like this one...at least my brother did.
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Wario Ware: Smooth Moves - This is another one of those group games that will have you splitting your sides from all the laughing. I think it's more family friendly than Raving Rabbids but both are fun.
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Wii Fit - Good luck finding one! =P Some of the games are pretty fun even if you're not looking to lose weight or anything like that on this game. Lots of fun with a bunch of people...but the game kind of goes nuts if different sized people jump on and off in the same session. Calibrations will probably be off every time a new person starts playing. Personal favorite is the hoola hooping game. =D
I think that's all the ones I've played. No real "favorite" (unles you count my biased love for everything Harvest Moon), just games I would really rather play than others. Getting a nice balance of single and multi-player games is definitely a good idea. The Wii is really made for multi-player rather than single player, unless you're by yourself like I am. =(