I've played a bunch of DS RPGs. As was said already there's a ton of them, as well as all the ones for GBA, and lots of lists and guides online to help you pick out ones you might like.
As far as what I've played: I really enjoyed Etrian Odyssey - the option to draw your own map and write notes and so on as part of the game was great, that is, great if you have fond memories of slaving away with a book of graph paper making a complete map of The Bard's Tale, for example. But you also have the option to have the map (mostly) autocomplete itself so it isn't a chore if that's not your thing. There's lots of secrets and things to go back and discover, as well as character classes you might not get to use the first time through... I have a feeling I missed quite a few secrets along the way. Oh, and it is HARD. Fights are brutal! I see there's an Etrian Odyssey II in the works.
The port of the cel phone RPG Orcs and Elves (by John Carmack of Doom fame) was fun as well, if a bit short. (Actually if you are looking for a cel phone game for some reason, I recommend both Orcs and Elves 1 & 2, as well as the Doom RPG. Those kept me occupied during many downtimes at work and so on).
The Final Fantasy games for the DS all look really great; I got quite far in FF3 but got distracted and forget what I was supposed to be doing, which pretty much is what has happened to me with every single FF game I've tried to make it through.
Dungeon Explorer: Warrior of Ancient Arts didn't give me any satisfaction, I stopped playing it after about two hours and don't feel any interest in going back to it. There's nothing really wrong with it, it just felt like a button masher and the story didn't interest me.
Mystery Dungeon: Shiren the Wanderer is a pretty straightforward port of the old SNES game of the same name, which I loved. It looks great on the DS. However it is also extremely hard and could be really frustrating if you don't like roguelike type games where death literally could be waiting at any turn, no matter how tricked out your guy is, with no save option. Oh, and of course you might also just starve to death.
I'm excited about the port of Mazes of Fate for the DS, but it looks like the release date has been pushed back.
I also started playing both Luminous Arc and Rondo of Swords, but haven't had time to form much of an opinion about them. They are both tactics games. I think the Ogre Battle games and Final Fantasy Tactics have made me really picky about that type of game; neither Luminous Arc or Rondo have really grabbed me so far.
Zelda: Phantom Hourglass was a really fun game. I also really liked Professor layton and the Curious Village, not an RPG though.
I think that's it.