(3)DS is the best system EVER! I love it soooo much. Here are some of my favourite games and why.
Note: Check out http://www.metacritic.com/browse/games/release-date/available/3ds/metascore and http://www.metacritic.com/browse/games/release-date/available/ds/metascore as well. You might have more variety in your game choices than I do, and there are lots of other games rated in the 80s+.
- The Legend of Zelda: A Link Between Worlds: This game is sooooo good. Totally reminds me of SNES-style Zelda, and unlike most of the O&@#ing Zelda games on 3DS / DS, this one is an original game and not a remake.
- Various DS Castlevania games (not the 3DS one! That one SUCKS!): Horror / exploration. You're in an enormous castle and need to find your way around, but certain paths are blocked off to you until you beat bosses and then obtain a new power like, say, the ability to slide into narrow passages. If you ever played Super Metroid or Super Castlevania on SNES, that's basically what these games are like.
- Various Mario & Luigi games: These are a fun romp. Humourous, RPG elements. You need reflexes for these though, because you actually have to time e.g. the stomp on the enemy's head or the block when something's coming at you, so they are not my favourite. :D
- Etrian Odyssey series: These are one part old-school dungeon crawlers ala Wizardry / Ultima and one part CARTOGRAPHY! The bottom of the screen is a little map that you fill out as you get deeper and deeper into the dungeon. It is unforgivably hard, so don't buy these unless you enjoy dying A LOT. But when you get past certain things, it's sooo rewarding. :D Here's me nerding out on EOII: http://webchick.net/node/61
- Bravely Default: The first half of this game is kick-ass Final Fantasy SNES-esque gameplay. Then the second half is absolutely offensive repetition. Play the first half. ;)
- Phoenix Wright series: In these games, you play a scrappy defense lawyer trying to defend their client. Characters and dialog are hilarious. Not much "strategy" really; mostly clicking through the story and paying attention at various places, but still tons of fun.
- Professor Layton series: In these games, you're a professor with a side-kick kid and you go jaunting about solving mysteries. The currency of the game is puzzles, so in order to progress in the game you need to solve them. The puzzles range from math and logic conundrums to slider block puzzles, etc. and start out easy but then get tough as nails by the end. Highly recommended.
- Picross: Combines logic puzzles with drawing. What is NOT to love about that, I ask you? Basically, there's a grid with numbers on the outside which indicate how many squares in the grid are chiseled and not. You need to work out where the chisel marks go, and at the end you get a picture of a fruit or whatever.
- Scribblenauts: This game is completely unique and totally lovely. You begin each level with a goal. For example, you're sitting on the ground, and you want to get an apple from a tree. Then you start typing names of anything you can think of. Say. "Chainsaw" to cut down the tree. Or, "Rope" to climb the tree. Or whatever. And POOF there you go you get a chainsaw or rope and can start using it. I'm making it sound really shitty, but it's actually fun. :P
- Advance Wars series — Turn-based strategy game. Fight enemies with tanks and shit.
- Fire Emblem series - Turn-based strategy game. Fights enemies with swords and shit.
- Civilization Revolution — DON'T play this if you can/have played the PC version because the starkness in graphic shittiness will make you vomit. however! It's a great way to kill ~4 hours on a plane by decimating the entire planet as the Russians or whatever.
- Super Street Fighter IV: 3D Edition: Because I can totally kick your ass with Chun Li. :P
- Nine hours / Nine Persons / Nine doors & Zero Escape: Virtue's Last Reward: These might be hard to find. It's basically crazy, fucked up Japanese murder mystery "Choose your own adventure" style game that has like 9 different endings. 999 is the orignal (DS) and Zero Escape is the sequel.