Make sure you install CFW so you can play for free.
Kid Icarus Uprising
Etrian Odyssey IV
Tales of the Abyss? (PS2 version is probably better, not sure if there's an undub of the 3DS version that keeps the voice acting for the little bonus cutscenes or not)
Persona Q if you've played 3 & 4
the Pokémon games (from oldest to newest pick one from XY, one from Omega Ruby or Alpha Sapphire, then skip Sun and Moon and pick one from Ultra Sun or Ultra Moon)
(if you only want to try one I would recommend USUM or ORAS)
The Ace Attorney series, if you've never played one before download the trilogy, otherwise you should be able to figure out for yourself. Also newer games such as Dual Destinies have DLC you should pirate.
Professor Layton and the Miracle Mask (the DS games before it are good, but Layton 6 and 7 are bad and not worth playing)
Quite a few rhythm games if you're into that (Rhythm Heaven, Miku Project Mirai, Theaterhythm, Rhythm Thief, Harmoknight, I'm not into these though so I can't say for certain)
Various Dragon Quest remakes, with most you'll want them patched so they can be uncensored or have the original music or just to play them in english, there's also the best version of XI if anyone ever releases a fan translation
Fire Emblem games that aren't Fates (pirate the DLC)
Hyrule Warriors (pirate the DLC, also don't get it if you don't have a New 3DS since older models can't handle it)
the remakes of OoT and MM
Xenoblade Chronicles if you have a n3ds can't play the slightly better Wii version for some reason
The port of Donkey Kong if you haven't played that on the wii either.
The remake of Metroid 2
Kirby Games
Super Mario 3D Land
Mario Kart 7
There's a remake of Devil Survivor, I played the DS version of that and it was pretty good, get the undub.
It can also emulate stuff like GBA and SNES pretty well.
I know there's more stuff and if I remember I will post, I'm generally trying to only recommend things I've played though.