When we got Isabella, we always figured we'd call her Bella for short, but that never happened-- other people are the only ones that call her Bella. She's always been Isabella to us. She's gotten a few other nicknames over time, however, as has Jake.
Baby Girl -- the most common of her nicknames and used almost interchangeably with Isabella; sometimes I think she responds better to this than her real name
Missy-- usually used when she's getting a little brave (as in, "You better watch it, missy")
Princess-- used when I'm pretty annoyed with whatever she's been doing (typically because she's acting "too good" for something)
Jake-Jake / Jakey boy-- most common nickname and usually helps entice him to come on over and do something
Big Boy-- a typical nickname my husband uses; he's going to be bigger than his sister one of these days, so it fits
Goober-- used when he does something goofy or klutzy; one of my husband's favorite nicknames for him because it fits so well