Wario Ware isn't really a game to play by yourself, technically. You play through it initially to unlock multiplayer mode, but from that point it's really more of a game to play with friends. The microgames (as they're called) only last about 5 seconds each, and they come at you rapid fire. There's about 200 unique ones, and each one has slight variations... possibly 1000's of variations... like one where you have to shine the spotlight on someone, each time you play it, they'll be in a different place... so it's the same game, just a variation (ie: you won't be able to memorize exactly what to do and when).
All that said, it's a spectacular party game, and allows up to 12 players to join in.
Rayman also is one that isn't really meant for single player action. There's not much of a story, and it's essentially around 70 mini-games. You do have to play through the single player portion to unlock all the games, and most of the multiplayer is of the "pass the wiimote" variety (though some minigames allow 4 player simultaneous).
The difference between the two games, Rayman's humor is in numerous ways you get to smack around the rabbids. Wario Ware's humor is in watching your friends do all the goofy ass forms to complete the microgames.
Both make great party games (and although not really a party game, Wii Sports is always a big hit when I get together with friends as well... but Wii Sports is also a good single player game with a surprising amount of depth that you won't notice if you just play it once and put it away). I've got both, and I think they'll be a permenant part of my collection.
If you're looking for some good single player games (that could also be multiplayer, like Madden), if you like racing games, especially arcade style, Excite Truck is pretty damn fun.
There's also Red Steel for another FPS. Controls similar to Call of Duty, but it is a little more ... exact? It's kind of a love it or hate it game, and the main point of contention is the controls. I personally like it, but there's a lot of people that don't. Definitely give it a rent at least, and see if it fits your tastes.
Another FPS is Far Cry Vengeance, but it's been almost unanimously abhored by press and gamers... so rent at your own risk.
Also, I really shouldn't have to mention Zelda. Unless you're just completely opposed to action/adventure games... you really can't go wrong with Zelda.
If you like quirky games, Elebits is pretty fun. It's probably more of a rental though, as it's a pretty short game. It does have 4 player simultaneous, but it's pretty weak, and seems to really only be there as a bulletpoint for marketing. It does have some nice physics, however, and as you progress through the stages you unlock things that allow you to build your own stages. I've seen youtube videos of people doing things like domino's and Rube Goldberg machines, similar to some Half Life 2 videos when people got ahold of it's level editor.
Other games I hear are good, but have not played them myself, Super Swing Golf (fantasy golf sim, more in depth controls than Wii Sports Golf), Trauma Center (surgery sim), Super Monkey Ball (puzzle/maze game, actual game plus 50 minigames as well),
Wii Play (a collection of games similar to Wii Sports, one of which is the Target Practice one, that has a Duck Hunt mode) is also due out early this month, and will have a wiimote packed in (it's kind of like buying the wiimote and getting a game for $10).
There's 12 other confirmed releases for Q1 (through March 31st). SSX Blur (snowboard racing / tricks), Blazing Angles (WWII flight combat sim), Prince of Persia (action/adventure/platformer), Tiger Woods 07 (a more complete real golf sim that plays similar to Wii Sports Golf), Medal of Honor Vanguard (WWII based FPS that graphically looks far better than Call of Duty 3), The Godfather (FPS), and Sonic (platformer)... are the ones that interest me most. TMNT might be good too, it's shaping up to be an action/platformer along the lines of the last Ninja Gaiden on Xbox.
Bust-A-Move is a puzzle game (in the vein of Tetris, Hexic, Bejeweled, Puyo-Pop, Dr. Mario... etc, etc, etc), they tend to be well recieved though I've never played one, so not really anticipating it (even though I do enjoy puzzle games on occasion).
Bionicle and Disney's Meet The Robinson's don't really hold an interest for me.
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