Depends on what your preferred genre is.
RPG: Fire Emblem Awakening is a must own and I also recommend Devil Survivor Overclocked. But 2013 is the year of RPGs so if SRPGs aren't your thing, their is a Tales of Abyss port available, if you like old school first person RPGs, Etrian Odyssey 4, Soul Hackers just came out which is a updated remake/port of a Saturn/PS1 game but Shin Megami Tensai 4 is coming out this summer if the slgihtly older look or feel doesn't work for you. Unlimited Blade is on eShop and is decent. Monster Hunter 3 Ultimate if you prefer action mixed with RPG elements. Kingdom Hearts Dream Drop Distance, Project X Zone and if you can wait there is Mario & Luigi: Dream Team and Pokemon X and Y much later in the year..
Action: Kid Icarus Uprising is a must own IMO, Resident Evil Revelations is another great game (and due to the HD ports this year selling pretty low now). Shinobi if you like challenging 2D platformers. Code of Princess is a anime style beat em up in the vein of Treasure's Guardian Heroes game. There are 2 version of Cave Story with 3D implementations (retail with polygons backgrounds and characters and sprite version with 3D background elements). Liberation Maiden is pretty dope, even if it is short and potentially touch screen destroying if you are rough with it.
Puzzle: Pushmo/Crashmo available on eShop, Tetris Axis, Luigi's Mansion: Dark Moon is sort of a puzzle game. Mighty Switch Force is a platformer with puzzle elements. A bunch of eShop games I haven't even sampled. Zero Escape: Virtue's Last Reward (one of the best stories ever put on a video game, also check out 999 on the DS), Professor Layton: Mask of Miracles is available as well.
Honest, unless you prefer First person shooters, realistic racers or dating sims (and are outside of Japan), I can't think of a genre that isn't represented in some way on the 3DS at this point.
Personally, of this year's releases Luigi's Mansion Dark Moon and Fire Emblem Awakening are the best most recent releases. But as I said, depending on you preference and budget you have options.
