The World Ends With You - One of the best RPGs I've ever played.
Phoenix Wright: Ace Attorney - You can ignore the Ace Attorney games after the Phoenix Wright trilogy, but these are some of the most unique, charming, awesome gaming experiences out there.
Legend of Zelda: Phantom Hourglass and Spirit Tracks - Great additions to an awesome franchise.
Hotel Dusk: Room 215 - A unique film-noir-esque detective story you won't soon forget.
Elite Beat Agents - Some of the most insane, wacky fun you will ever have. Ever. An absolute must-have time waster. Think Dance Dance Revolution on the touch screen, but more than just the four buttons. All over the place. Awesome.
Final Fantasy IV - A well-made update on the first truly great entry in a legendary franchise.
Chrono Trigger - A mostly faithful remake of one of the greatest games ever made.
Advance Wars: Dual Strike - One of the most addicting games ever made, and my personal favorite turn-based strategy game ever. For that matter, I hated the genre until I played this game. Holy crap it's awesome.
Puzzle Quest: Challenge of the Warlords - This is available on many systems, but you may as well get it here if you haven't yet. It makes a Bejeweled-esque puzzle system into a much more complex and awesome RPG battle system. Seriously. If you think that sounds awesome, it's even moreso.
Meteos - A falling-block puzzle game with an awesome twist; as you line up three blocks, they jet into the sky, and you have to keep matching blocks within the pile until it launches off the screen. The physics are different depending on the size of the pile and even the gravity of the planet you're playing on. It's a simple puzzle game, but an addicting and awesome one. Also, the Disney sequel didn't happen. I don't even know where I just came up with that idea. It would be stupid and whoever would make it should die.
Time Hollow - Moreso than Phoenix Wright, it's an example of a visual novel, a genre that is mostly lost outside of Japan. Shame; it's really interesting. This game in particular is just really awesome. I enjoyed it a lot.
Castlevania: Dawn of Sorrow - If you haven't played the exquisite Castlevania: Aria of Sorrow on the GBA, go play it now. Then get Dawn of Sorrow, it's direct sequel, on the DS. Two of the best side-scrolling games you will ever play. Ever.
I might remember more; if I do I'll add them in. The DS is quite possibly my favorite game system ever due to its huge library of absolutely amazing games. I freaking love it. All the above games are more than worth owning, even if some of them may be kind of difficult to find.