I'm 26.
I would suggest:
Mario Galaxy:
This game is a great example of the Nintendo mindset for games. A not-so-hot "casual" gamer could probably finish the game with just a little bit of effort. But getting 100% is no easy task.
Zelda:
Not sure why some people rag on this game. This has some GREAT boss battles (Undead Dragon anyone) and a huge environment. It was not repetative or boringly derivative for me at all, and I have been playing zelda games from the beginning
RE 4:
If you never played it on the GC it is an absolute must. If you did, it still may be worth picking up as the new controls bring a new gaming experience. Amazing game overall.
Zakk and Wiki:
While it has a colorful, cartoony look, this is no kids game. I can't imagine many 13-14 year olds who would have the patience to try to beat this game without running online to look how to solve every level. Death scenes are great too.
Mario Kart:
I know you said you weren't interested, but I really suggest getting this and forcing yourself to play with the wheel. Oddly, I have found that as I got older, I cared less (but not "not at all") about winning and more about having fun with the games. While using the GCN controller may make it easier, the wheel is a whole new experience and a whole lot of fun.
Battalion Wars 2:
Again, the cartoony look may turn some people off but this is a great game. Good strategy and action mix, and online is a lot of fun, if you can find people to play with (haven't been on in months, so idk if any one still plays)
Megaman 9:
A wiiware title, and well worth the money. This game is hard, even without trying to get the awards, or downloading the increased difficulty settings. Great fun.
World Of Goo:
Another Wiiware title that is a must have. Great puzzles and humorous/interesting design. A thinking game in a sea of mindless drivel.
That all being said, I haven't bought a game in a while, as I am saving my money for a house and engagement ring(hooray getting old) so I can't speak much about games that have come out recently.