It depends on what you like. If you like the psychological horror of a really interesting visual novel mixed with Escape the Room style puzzles and an incredible mystery to unravel, I recommend the Zero Escape series. It starts with Nine Hours, Nine Persons, Nine Doors, which is actually a DS game. However, the second and third game are both 3DS games. Virtue's Last Reward and Zero Time Dilemma, respectively. I actually prefer the first game, but they're all worth a play.
If you like Kingdom Hearts, Dream Drop Distance is fun to play. It's actually the only Kingdom Hearts game I've ever played; I played simply because the characters from The World Ends With You are in it, but the game itself was a lot of fun. The Fantasia level and the ability to play with the Dream Eaters were particularly enjoyable. (Speaking of The World Ends With You, it's a DS game, but if you haven't played it, you really should. It's really an amazing game.)
Pokemon goes without saying. Whether it's X and Y, the remakes of Ruby and Sapphire, or the new Sun and Moon... Well, Pokemon needs no introduction, really.
Legend of Zelda games are always good, too. Tri-Force Heroes is more like a puzzle game that you can play with two other people or solo. If you only have one friend to play it with, you're SOL, but if you have two you only need one cartridge and download play, so that's nice. I recommend Link Between Worlds, as it took my favourite Zelda game and remade it alongside a really neat twist of a play mechanic.
Classic platformers are always nice. I like Kirby: Triple Deluxe and Planet Robobot. I also love Yoshi's New Island, though not as much as the GBA version. Also, Poochie + Yoshi's Woolly World comes out on February 3rd, and if the demo's anything to go by, it's going to be so much fun.
And as a bit of a guilty-pleasure on my part, I always recommend the Cooking Mama games. They're fun and silly and good for when you want to play a dumb game for no reason other than to have fun. Nintendogs, too, for that matter.