Mine's Cinccino.
Most of my Pokemon experience is limited to emulators. The first real Pokemon game I got to play was X on the 3DS, and in that game, a friend of mine had Minccino in their Friend Safari. After I finished the game, I started to screw around with collecting whatever mons I could, and this little random Minccino, now evolved into a Cinccino, ended up as my main Pokemon Amie buddy. I think a lot of factors contributed to it becoming my favourite - for one, I really like Normal type Pokemon. I also like the evolved forms of popular stage 1 Pokemon; Raichu being a good example. I'd say Minccino and Cinccino are fairly equal in popularity though. It's also very well-designed I think. It manages to be both elegant and adorable, and... I mean, it's a fluffy mouse. What's not to like? And there's quite a bit of nostalgia attached to this as well, because my sister started playing Pokemon because of me, and she picked up a Minccino in her team after seeing mine in action. Its moveset and stats are shit, no doubt about that, though. But I don't play competitively, so that's of no concern to me.
I still have him in my save file, since I never bought the later games. I still open up the 3DS every now and then to pet him. So yeah, Cinccino.