The DS is nice if you like classic Japanese RPGs (Dragon Quest series, Final Fantasy remakes, Etrian Odyssey series), puzzle games (puzzle quest, layton series, even the ace attorney games can be called puzzle games of a sort), 2D Castlevania (three games of varying quality), challenging Mario games and Zelda. As a bonus you can play the very entertaining GTA: Chinatown Wars, which you can also get on the PSP.
I stretch my brain but... that's about it really. The DS kept me entertained for 3 years, but only with very select titles which I played and replayed several times over. Most of the above games I completed 3-5 times :/