I have one. Mario Kart is great, as is New Super Mario Bros. I want to get Brothers in Arms DS as that has supposedly the best graphics of any game yet for the system.
I don't use my DS that much any more though, the little time I have for gaming is spent on the PS2.
Excellent platform. Big Brain Academy or Brain Age is all the rage these days as a game. It also doubles as a controller for the Wii. Heck, you can get an Opera browser on the thing and surf the web!
Have a GBA never bought a DS my ex-girlfriend had 2 so I played hers.
Probaly my favorite DS game is Trauma Center: Under the knife. Its pretty tough though.
Some good GBA games
The Advance Wars and Fire Emblem games are my favorite GBA games. They are fun stargety games, everybody who plays them loves them too. I think an Advance Wars game is out for the DS now.
Zelda 2: Adv of Link - its the only Zelda game that I really liked. Its the side scrolling one that people hate.
Final Fantasy 4
Final Fantasy 6
Super Mario Adv. (SMB2) - the best Mario by far in my opinion.
F-Zero games