Recently I've been thinking a bit about fan fiction or "fanfic" and what role it has in the writing world. Going simply by submission for publication requirements one could hazard a statement of--not much. I suppose it can be a fun exercise, and I have nothing against people who enjoy writing it, but I've always have to wonder how I would feel if I saw my characters used in that way. I know there are authors out there that feel it is nothing short of robbery and that the fanfic writer is essentially putting words in their mouths. Not such a great thing, and I know personally I would rather not make an author I like hurt or angry. I'm definitely not in the position of ending up with fanfic right now, but I do imagine if I ever was in that position I would probably end up putting my fingers in my ears and screaming "I'm not listening" if someone came to me and said "Hey have you seen that story where your main character *bleeps* Spock with a *bleep* *bleep* *bleep* rubber spoon."
There is more than one type of fanfic, though, and this one doesn't so much involve co-opting someone's characters as much as someone else's world. In a way you could call it "role playing". There are actually several successful authors that write in worlds that are not solely their own--Salvatore comes to mind for one (and I rather like him). But if you're not Salvatore, will this type of writing help you as an author? Well, character studies are never a bad thing, and if you have a background to work with it makes it quite a bit easier, but the problem that comes up with this form of fanfic is that most editors really do not want to see you write a story about your D&D, Shadowrun, or Exalted campaign. It's just that usually, those types of stories appeal far more to the players than anyone out wandering around the literary world. I suppose if you write it for yourself (as some people I know do) it can help you hone your writing skills.
I, personally, try to keep well away from fanfic in most cases. I figure that I can do my character studies in my own world (or this one) and that if it turns out I really super duper like it and want to try to get it published I don't find myself running up against the "do not want stories containing copyright material/D&D campaigns" wall. It's a personal thing, and I suppose some of it is due to the fact that I really want to get published and don't see writing something that is virtually unpublishable as very productive. But then again, even if I'm doing something just for myself I prefer it be useful--like a hairclip, so it's not so strange that I won't do something if someone (in this case me) isn't getting something out of it.