There are tons of great DS games! But what KIND of game are you looking for? Here's a run down of games I've I've enjoyed.
Legend of Zelda: Phantom Hourglass
Final Fantasy Crystal Chronicles: Ring of Fates
Advance Wars: Duel Strike
Castlevania: Dawn of Sorrow
Mario & Luigi: Partners in Time
Elite Beat Agents
Final Fantasy 3
Animal Crossing Wide World
New Super Mario Bros.
Then there's a bunch of other games that look great
The World Ends With You
Metroid Prime Hunters
Castlevain: Portrait of Ruin
Advance Wars: Days of Ruin
Final Fantasy Tactics A2
Ninja Gaiden Dragon Sword
Mega Man ZX
Pheonix Wright: Ace Attorney
I guess it depends on what genre you like. Everything is represented pretty well, except sports games.
Both Castlevania games (Dawn of Sorrow and Portrait of Ruin) would be at the top of my list. There's a 3rd Castlevania game coming out in the fall that I'm sure will be as good as the previous two. These games are like Castlevania: Symphony of the Night and not like the old school NES/SNES games. They're 2D Metroid style where the game is one giant map and you go around collecting items that allow you to reach new parts of the map, as opposed to hack'n'slash platformers.
Mario Kart DS is the best Mario Kart game ever released, though I understand it's tough to find now.
The Advance Wars titles are great turn based strategy games, but the board uses squares instead of hexes which, if you're anything like me, will drive you positively nuts.
Kirby's Squeek Squad is a great platformer, if a bit on the easy side.
Final Fantasy IV is a retranslated, modern(ish) graphics version of Final Fantasy II and every bit as excellent as it ever was.
If you want something completely different and incredibly fun, I'd recommend Elite Beat Agents above all others.
There are a ton of good choices if you bought a DS to recapture the 16- to 32-bit era, including the Castlevania games, New Super Mario Bros., Mario Kart DS, and the very awesome and ball-bustingly difficult Contra 4.