Hm, this is a good question.
In a suspense story I have in the plotting stages, the MCs all have various problems they are coping with. (More so than most of the characters in my children's stories) Collin is a recovering addict and alcoholic, which brings up a lot of interesting points with the characters. But with him, it's a major point in the plot.
My character Paddy was disrespectful and disobedient to his father growing up--eventually chasing his parent away--but for good reason, because his father was not a nice man and was a threat to the family. Paddy likes to break the rules, but for good causes. This background with his father, though, affects him in the respect that he just really, really wants to be a husband and dad--and to be the best one in the world, in spite of his father's example and to sort of "redeem" from what his family had to put up with.
I have another character who is vaguely alcoholic, but he doesn't see a problem with it, which is interesting to deal with, too. I've not written enough of this story to know how it ultimately affects him and those around them yet. A character in that same story deals with abandonment and is always ready to run off on people; he also holds grudges.
A lot of my characters seem to be chronic liars.

Not really sure what that says about me...