Everyone is likely gonna list the obvious DS games to get, and i'd agree with probably all of them. Anything with Mario is great, and the new Yoshi game is great although not nearly as good as the original. I'm gonna list what I think are some of the lost gems for the DS, and they truly are gems.
Yoshi's Touch & Go - People are gonna tell you this game is not that great. They're lying to you. It's literally one of the best games for the DS, if you're capable of getting into this type of game. It's basically one of those old school arcade type games, where it's all about high score. You can traverse any one of the 4 modes of play, and you're basically trying to get the highest score possible. I think it's one of the best DS centric games so far for the system. I'd love to see a Wii version, but the asshole review scores probably will prevent it from ever happening.
Pac-Pix - No, this game isn't as good as Yoshi, but it's still quite brilliant. Pac Pix, like Yoshi's T&G, can also be had for a very cheap price these days. Pac Pix basically has you drawing PacMan's on the screen, and they suddenly become alive and you manipulate them around the screen by drawing lines. It's really quite awesome, but it's just too short of a game. However, it really is one of those games that so cool that you might just find yourself playing it here and there for years to come.
I'd also throw in
Kirby:Canvas Curse, and
Wario Ware touched.