Being able to play Japanese exclusive games. As a big fan of the Theatrhythm games, I always wanted to play the Dragon Quest one, but couldn't due to it being Japan exclusive. Now I can thanks to 3DS modding. Another Dragon Quest game that comes to mind, since the 3DS had a ton of Japan only ones, is the remake of the first Dragon Quest Monsters game. I remember finding out about it from a friend around the time it came out, and thought it looked cool, but, again, had no way to play it, until now. Even beyond the 3DS' own library, playing fan-translated games from retro consoles is awesome. It feels so natural.
I also recently discovered the 3DS can emulate PS1, which is just so insane to me. It doesn't even sound real when I say it, but, lo and behold, it is.