Most fun games for Wii:
Mario Kart Wii: This game can be extremely frustrating, especially when playing online, but something about it keeps me coming back for more. This game is, in a word, addicting.

Super Smash Bros. Brawl: This is a great fighting game because it features classic Nintendo (and Sega and Konami) characters as the fighters, so you can play as your favorite video game character, from Mario to Captain Olimar to Link to Sonic to Solid Snake.

Guitar Hero III: Legends of Rock, Guitar Hero World Tour: The Guitar Hero series has always been great for individual play or groups. They have great songs including "School's Out" (III) and "The Joker" (WT).

Super Mario Galaxy: This is probably my favorite Wii game. It's insanely fun and really addicting. It's great for individual play, but you can also have two players if you want. I've said it before and I'll say it again: everything about this game is great, from the overall gameplay to the background music.

Most fun games for Game Cube:
Mario Kart: Double Dash!!: In this installment of Mario Kart you can have two players on one cart, which can make for some interesting pair-ups such as Mario with his nemesis Wario, Luigi with Baby Luigi, or the tiny Toadette with the giant Bowser.

Super Mario Sunshine: This game is the son of Super Mario 64 (N64). Mario is equipped with a water gun device that he uses to knock-out enemies and clean up graffiti. The only down-side of this game is the terrible actors that they used to record the cut scenes, but the gameplay makes up for this awkward acting.
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Mario Party is a very fun game, especially if you are with a group of non-gamers. The mini-games are fast-paced, easy to pick up, and anyone with just a little bit of hand-eye coordination can play it.

http://www.youtube.com/watch?v=LqDYbdf8YGc

http://wiispot.com/wp-content/uploads/2007/03/mario_party_8.jpg
Another super fun game for the Game Cube is Pikmin. Pikmin is kind of like that Lemmings game from the PC back in the day, if you remember that. You control these absolutely adorable primary-colored creatures, called Pikmin, to dig up things and fight things for you. There are many levels. Pikmin is impossibly cute, and easy to learn, but can get rather challenging towards the end. However, the learning curve is pretty gentle. And to play with the little Pikmin is so much fun!

http://www.youtube.com/watch?v=tEGnc4AXkSA

http://www.sonoma.edu/users/a/acevesm/graphics/pikmin.jpg
Source(s):
http://www.youtube.com/watch?v=LqDYbdf8YGc

http://wiispot.com/wp-content/uploads/2007/03/mario_party_8.jpg

http://www.youtube.com/watch?v=tEGnc4AXkSA

http://www.sonoma.edu/users/a/acevesm/graphics/pikmin.jpg

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Mario Kart Wii and Mario Party 8. If your playing alone, For something more adult, I recommend Resident Evil for the Wii

http://www.youtube.com/watch?v=R4oquHWBpLY
http://www.youtube.com/watch?v=Hv1eIN8RE7k
http://www.youtube.com/watch?v=sh_-jvhascE
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i think it depends on what kinds of games you are into, if you like RPG games, there is a wiiware final fantasy game that you can download where you get to build up your own kingdom, hire your team of fighters etc. there is also always zelda which is always one of my favorites. if youre into mini games, any of the rayman raving rabbids games are really fun and they really utilize the motion of the wiimote/nunchuks. animal crossing and paper mario are also some of my favorites for both consoles.
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