I'm a huge Mario fan, so I recommend lots of Mario games. Here's a list of the best ones, and why I recommend them:
Super Mario 64 DS: This game is just all-around epic. Great graphics, fun story, gameplay rocks. I've probably gotten hundreds of hours of gameplay off of it. The minigames require excessive use of the touch screen, BUT they're not part of the actual plot, so you don't have to play them if you don't want. Personally, I would, though...they're extremely fun and addictive!
Mario and Luigi: Partners in Time: Surprisingly good graphics, the story is enthralling, and the gameplay is just unbelievable. Also, I'd say it has the best soundtrack of any Mario game other than Super Mario Galaxy. Also, aside from one extremely brief scene, the game doesn't use the stylus at all, so it's screen friendly. My only problem with it is that it's a tad shorter than its predecessor, Mario and Luigi: Superstar Saga. If you have a basic DS or a DS Lite, I also recommend you get that game too.
Mario Kart DS: Nice graphics, addictive gameplay, and it has extremely high replay value, because there's so much to do, and, once you've done it all, so many records to break. Also, most stylus commands can also be done with the buttons, so it won't wear out your screen.
Super Princess Peach: Probably not as much replay value as the previous three, but it's a charming platformer all the same. It's very long and filled with unlockables. You do need to use the stylus to swap out Peach's vibes or play the minigames, however.
