I tend to have a pool of characters that I cherry pick from, mostly because those characters tend to already have a fleshed-out backstory that doesn't feel forced, even if I have to tweak it slightly to fit them into a slightly different time setting.

[s]I also suffer from "favourite child syndrome" oops[/s] What? I mean, I just have certain characters I never get tired of playing/writing as, that's all *whistles innocently* 

That's not to say I'm not capable of making up an entirely new character if I have to, just that most of the time one of my pre-existing ones are more of a go-to.