Dragon Quest IX, easily. That game was glorious.

Try Rune Factory.

Children of Mana, Sonic Chronicles, and Kingdom Hearts Re: Coded.

I respectfully disagree.

Seconded. I'm not too hot on those games.

Jeez, three years since I last posted here. How times have changed. I guess I'll just list them off.
1. The World Ends With You
2. Radiant Historia
3. Shin Megami Tensei: Strange Journey
4. Shin Megami Tensei: Devil Survivor 2 (more of an SRPG, but it has traditional elements in it)
5. Suikoden: Tierkries
I also like Super Robot Taisen: OG Saga the Endless Frontier, the Mario & Luigi games, and Might and Magic: Clash of Heroes (although that's more of a puzzle game). I like Pokemon too.
To think, I hadn't played a Shin Megami Tensei game three years ago. How empty I must have been.

Also, in before Waltz comes in and says "none, because there are no RPGs on DS. Real ones, anyway."

Mario And Luigi: Bowser's Inside Story

From what I've played:

8. Glory of Heracles - the only game I wouldn't really recommend. As far as mechanics go, it's solid, but I found it to grow boring eventually, because there isn't much variety in the game (the towns all look the same...). I suppose it would still be worth a look if you found it cheap, though.

7. Fire Emblem: Shadow Dragon - I don't know what it is, but after coming off of Sacred Stones, it just seemed somewhat dissapointing. It's still a fun game, but don't expect expect anything modern. It may be a remake, but the graphics are the only thing that have been upgraded. This is still a brutal NES era game underneath.

6. Nostalgia - I haven't played an RPG quite as unique as this one before (as in set in an alternate version of the real world, visiting exotic locals such as El Dorado, Noah's Ark, Mt. Fuji, Pyramid of Giza, and more), but for some reason, it isn't nearly as epic as it should be, and the characters are pretty generic (which is a shame, because they have some pretty great side stories), but the gameplay itself is really solid, so it's still very much a recommendation.

5. Lufia: Curse of the Sinestrals - This is a pretty great action RPG, with interesting enough characters & story (it probably would be higher, but you have to play through it twice to get the "good" ending).

4. Suikoden Tierkries - This takes a more traditional approach (random turn based battles), and is darn good at it. It has an intriguing story, lots of playable characters, and high production values (voice overs & anime cut scenes).

3. Kingdom Hearts: 365/2 Days - Not as good as Re:Coded, IMO, but it's still a very solid action RPG. It's more for those who know KH's story though.

2. Mario & Luigi: Bowser's Inside Story - If the only RPG's you've ever played are the Pokémon games, this will probably be one easiest for you to digest, which is fine because the story is humorous, and it's mechanics are solid.

1. Kingdom Hearts: Re:Coded - I honestly don't see how people can like 365/2 Days more. I've been a huge fan of KH since the original, and this one captures the magic of the series much better than 365/2 Days does.

This is a tough one.

I haven't finish Radiant Historia yet but if it does not derailed in the second half, it is a contender.

The World Ends With You would probably be my choice. It has it all, graphics, music, story, characters, fun combat, style, innovation... you name it.

My most played ds game is Dragon Quest IX by a landslide. Great game. DQIV is also very good and charming.

Chrono Trigger doesn't need presentation.

Valkyrie Profile has a great setting, dialogues, fun combat system and interesting story (but uninspired ending).

D*** it, there are too many. The list just goes on and on and on.

Somebody really needs to take a spin with this game!

The World Ends with You and Solatorobo are my picks.

I also happen to like Lunar Knights, but that seems to be a different thing.

Chrono Trigger and Final Fantasy IV are the obvious best ones. But since one's a port and the others a remake they're excluded from me. My favourite original DS RPG is The World Ends With You.

Keep in mind that, at least from what I've read, you might not get that much out of the Kingdom Hearts games unless you've played others in the series. I've thought about getting them before, but I haven't played any of the others and decided to pass.

While not strictly an RPG, I'd suggest checking out Might and Magic: Clash of Heroes. It's a great little game, and doesn't get talked about as much as it should.

The Glory of Heracles, Infinite Space, and Nostalgia I liked. Of those Infinite Space is my favorite, pretty long and hard game. The others were too short to be considered that great.

Something tells me your favorite game is Star Ocean: Till the End of Time.

@TheConsonant I played Infinite Space for a while, until I accidentally saved before a plot boss battle underlevelled and found no way to advance aside from deleting my data. I was about six hours in, and I couldn't be bothered to start it up again.

It was a real shame too, since what I had played so far was really promising

Nope. I've never played a star ocean game.

The Dragon Quest games are awesome remakes too. The best not-a-port DS RPGs I've played would probably have to be Radiant Historia and Dragon Quest IX.

I rented Clash of Heroes for the DS and really enjoyed it. I would have picked up a copy but I decided to go for the PC version instead.

Hard to say. Still a few good titles I've yet to give a try. A lot of disappointing ones for me (namely GS: Dark Dawn and both FE games) but I think it would probably be Radiant Historia. The whole time travel aspect and redoing past events was somewhat innovate (at the least the way it was implemented) and one of my favorite parts of the game. OST is pretty top notch too. SRW OG: Endless Frontier is up there too.

I've had Lunar: Dragon Song sitting in my collection for about 3 years and haven't touched it yet. ;D I hear it's awful, but still gotta get around to at least trying out.

RADIANT HISTORIA.
Amazing game. Great soundrtrack too.
If you have a sudden aversion to it, play BiS.

Now that I have finished it, I have to include in my list the great Radiant Historia.

Atlus, give us more original games like it! (For the 3ds, please).