In my past experiences on New Leaf, I've had:
M-puff
Maddie
M-cat
I'm sure there are more, and I remember a lot from Wild World, but I don't want to mix them up. xD I'll edit this post if I remember any more.
Oh God... I've had sooo many nicknames, it's not even funny. Sweet C, Mega C, Fancy C, Little C, L'il C, Dr. C, Sugar C, Wonder C, kiddo, hun... I'm sure there are more I'm forgetting. I think my favorite nickname, though, was the one Puddles came up with for my alt: shmoopy. WHY did she have to give that to my alt; I would have much preferred it on my mayor, that name is amazing.
Cupcake, Muffin, Junebug, Dearie and Pop Star. Those are some of the old nicknames I'd received. The one being used right now is "mon amie". Marshal started it.
Because of Stinky, everyone is constantly calling me Beefcake. Other names have been floating around, but Beefcake always comes back sooner or later XP
since i play a Japanese game but have an English character name (Skye), my nicknames are always messed up. They often try things like taking the last or first two characters and then adding っこ(-ko) or っち(-chi) to the end... which produces things like yeっこ or Skっち.
Yeah. No. I just tell them to call me Su most of the time. I wish my villagers would come up with things like Shorty and Cupcake!(  ̄д ̄)
The first one they suggested was "big guy" I was like sure.. I mean I'm not even big physically but as a mayor, hell yea I'm big, making all those PWP's and getting the town to look good! LOL.
Then I think Gwen called me Young T and I was like, this seems like a sweet rapper name, alright, done. So some people call me Young T, the majority call me big guy.
Flora asked for a custom one and I made her call me "m'lord", haha. It hasn't spread around yet but I hope it does, soon all my villagers will be calling me m'lord and I'll truly be the king of my town, harhar.