Pokemon X. I received my 3DS on Christmas 2013, and Pokemon X was one of the games that came with my 3DS. Activity Log says that I have logged about 350 hours of playtime on that game, which sounds a bit high to me.
Mine was Super Street Fighter IV since I got my 3DS at launch. I think I played it for like three days before passing it off to my younger brother, ha ha.
I think my first game was Pilotwings Resort, I probably had the Mario game that released when the 3DS released as well, I usually don't play those kinds of Mario games as much as I should though.
My first 3DS game was Pokemon Rumble Blast. I picked it back then because it looked quite interesting.
Overall, it was a pretty good, I had lot's of fun with this game.
Even though I was planning to get New Leaf as my first game on 3DS, I didn't manage to find it anywhere at the time so I bought Pokemon Omega Ruby instead. I hadn't played Pokemon games before either so it was a great experience!