Well, for me it was a bit odd... I started off with a typical Troll Goon, then decided to put him in a Mortimer of London suit because it had good armor and a concealment bonus like the Lined Coat. Then, when looking at vehicles, I decided to go with an SUV and give him some points in Pilot Ground Vehicle, because when I was playing a Premade and nobody in the group knew how to drive. I called him Enzo, just because I like the car. A bit of play later and I ended up getting called Softy by one of the group, and I quipped back "That's MISTER Soft to you!", and boom, the character was well and truly born.
I'm sure everyone here knows the feeling; when a character takes on a life of their own, and you just know what they'd do, regardless of if it's the best move or not.
As for his actual growth as a character... he started off in my head as just a mob-connected thug in a suit, but developed quickly into a ruthless, merciless, utterly amoral professional hitter and wheelman. The kind of guy who'll break a couple of your fingers before he starts asking questions, just to prove he's not bluffing.
Currently, though, I'm playing a Pixie that goes by Finn. Started with the incredibly original concept of a Pixie Mage (yes, I'm being sarcastic) and ended up with a real handful that is, in many ways, worse than Mr. Soft.
Soft is a cold-blooded murderer, but Finn... Finn's just nuts. He's not a monster like Soft is, but Finn really, really enjoys screwing with people's brains and causing mischief and mayhem for the sheer joy of it. The one time he ended up doing an actual Good Deed (destroying a bunch of Ghouls that were selling their leftovers to Organleggers and rescuing their remaining living victims) he actually had trouble wrapping his head around the concept of having done something beneficial to society.
So, yeah, my characters tend to get away from me a little.