I really don't have a good answer for that. I tend to think about my current story/characters when I'm at work, but obviously I can't be thinking about it all the time I'm working, either, otherwise my job would suffer. But when things are slow, nothing keeps the time moving like hashing out a plot point or figuring what hobbies a character would have, what kind of food they like, etc.
And I'm kind of coming up a blank on a good story for the second part of this question. I mean, a lot of my stories use elements taken from my life (especially music choices and the like), so there are plenty of things IRL that make me think of my stories. But I guess this sort of counts: I once bought a plush owl because it kind of looked like a character from my 2007 NaNoWriMo (even though the character wasn't an owl).