I typically draw character I use in role plays, but never anything as advanced as a scene or panel of a comic. I also find it helps me to visualize my character better, and describe them in more detail.
A lot of my characters are based off of songs, things I've seen in TV, or something I've read in a book. Sometimes I'll be drawing and I'll make something new, and then that picture becomes a character concept to be developed... :)
For me, i hate it when characters are clearly just a skin for their builder. Like, if we're role playing (in person or online) and I know you personally, i can tell when you've simply slapped a name and design onto a piece of paper and called it a character, when its really just the player's...