When Aaron was very little, just a couple weeks old, he'd stare at something for a long time, studying it, and then blink in slow, methodical blinks. It was so cute - I thought he looked like a bug. So that is what I began calling him...my little bug. Every once in awhile it comes out "Bugs" but any reference to a Warner Bros. Character is strictly accidental. Hopefully it won't stick through his whole life and become an embarrassment to him.
I didn't really HAVE a nickname, unless you count "Jenny" but I don't happen to think that counts.
Does your family do nicknames?