The 5 DS games I consider must haves are:
1. New Super Mario Bros. -It's just good. It's not the best Mario platformer, but it's still amazingly good. Just don't expect it to top Super Mario World or SMB3 and you'll enjoy it.
2. Phoenix Wright: Ace Attorney- You can't go wrong with either one of these, but I personally prefer the first one.
3. Meteos- This was the first game that made me happy to own a DS. And it's still the best puzzle game on the system, and is definitely worth owning.
4. Castlevania: Dawn of Sorrow- Just like Phoenix Wright, both of the DS Castlevanias are worth owning. But I prefer the first one, just because I like the soul system. If you like the recent Castlevania games though, you'll want both.
5. Elite Beat Agents- Possibly the best DS game released last year, and for that matter it may even be the best DS game period. This is a game that truely has to be experienced to understand it, as the concept sounds incredibly stupid, and the soundtrack is enough to scare most people away. But if you give it a try, it's amazingly good. Also the Japanese version of this game, Ouendan, is definitely worth importing if you like EBA.
And if I could recommend more than 5, I think Mario Kart DS would be next(as it's the best Mario Kart ever), and Kirby Canvas Curse would be right after that. And then there are plenty of other great games beyond those, but those are the must haves.