When I'm playing I try to sit down with the GM and work up a story we can both use, and when I run I try to do the same with all my players. It helps get the appropriate feel and gives us material to use to expand the story.
Maybe at some point I'll explain the stories behind my namesake character, or my friend Dan and his wife in a few of our games... As a GM I love to have those backgrounds to use when I need a story on short notice and I'm running low on ideas.
