Well being "over 20" isn't really much help, except for the fact that it will take away all the "Kiddy Crap" that's out there as I guess you don't have and Kids yet, or a wife for that matter to consider when buying Wii games...
Tell me first though, you are really just a 14 YO kid wanting some "Mature" type games for your Wii your parents bought - aren't you... Jk!!! lol.
I've been gaming since the G&W generation so I personally find the Wii to be a "new" experience for playing as I'm tired of the usual way. (don't get me wrong, I still enjoy the PS3 and 360 too, just not as much).
Anyway, I have a wife too, so a lot of my considerations include her, but I'll list what I've played that I have enjoyed:
Zelda - Loved it even though it's also on the gamecube (never owned one so it was new for me)
Geometry Wars: Galaxies - Great for multiplayer arcade action if you can get it for < $15US
Zack & Wiki - Great game, especially if you like the old school point and click adventures, with a bit of 3d for depth.
Metroid Prime 3: Well, the Best FPS, controles and all, to date on the Wii
No More Hero's : A Great beat-em-up type game.
Resident Evil 4 : Another Gamecube game but it was new to me... and VERY awsome!!!
Star Trek Conquest: I'm a ST fan so hey.... It's a little crappy if you don't like this type of Genre but I love it anyway.
Little Kings Story: WOW - Just go ready my Review in the User review section on this site.
Mario Galaxy : Must Buy... Most played game to date for me (and my wife).
Mario Party 8 - Great for 4 player get togethers, esp with couples.
Other games I'm looking forward to that will be out soon:
The Conduit: enough said.
Indiana Jones ATSOK : Damn, i'm getting this JUST for the "fate of atlantis" origional point and click, Guess I get the game itself as a bonus... and co-op story game too!
That's about it from me... Hope you find something you enjoy.
It's me... no really, it IS me!!!