My husband and I have never actually taken the step of becoming co-authors, but we might as well be. When we work together, we basically brain storm and bounce ideas off each other until we hammer out a plot, characters, and logical motivations. I know you're probably thinking, "Um, that is co-writing" but when we do this, it's usually when I'm revising a second or third draft. I come to him and say "Look, X, Y, and Z has happened and now I don't know what to think" and we start hashing it out.
I have a friend I would love to write with, but I don't think she will go for it. She creates wonderful words and characters. I have a really, REALLY hard time creating context and setting for my stories. I usually have to do it in the second and third drafts. However, she can't think of a story--which is my strong point and generally what I care about the most. I think writing a story in her fantasy world would be a lot of fun, but I can imagine a lot of horrible things happening as a result.