LogFAQs > #979604952

Seconding Ghost Trick. Thirding Phoenix Wright Trilogy (Ace Attorney) as well.

Theatrhythm: Final Fantasy Curtain Call is another must, even if you've only played one or two FF games. Nobuo Uematsu is an amazing composer, and this game lets you experience so much of his work.

Elite Beat Agents, and Rhythm Heaven are also great choices if you like rhythm games.

Also seconding Lost Magic. Fun strategy game that makes excellent use of the DS's drawing feature.

Then there's Okamiden, though I'd suggest you play Okami first if you haven't already.

Then, of course, there's The Legend of Zelda: Link Between Worlds. A wonderful sequel to Link to the Past.

There's a good set of remade Dragon Quest games for the DS/3DS as well.

Furthermore, if you never had a Gameboy Advance, there are a bunch of games from that console that can also be played on a 3ds (though I consider a Gameboy SP to be the best console for GBA games). There's the Golden Sun series, Robopon, Pokemon Ruby/Sapphire, Boktai, updated remakes of the Breath of Fire and Phantasy Star series, Fire Emblem, and so much more.