I'm a student (actually, my official major is Computer Engineering, but my school, RIT, has a film department, so I take a few classes from there). I'm mostly into doing indie stuff (I guess that would be narrative?), and a bit of documentary stuff. If I buy a car by the end of the summer, then I'll offer local bands and such my services to make music videos and such. Oh, and I've also dabbled a tiny bit in some formalistic stuff (not really sure what category that would be under).
So I guess I'm all over the place as far as what kind of videographer I am. I have never done, and don't plan to do in the near future any wedding work because I don't think I'm talented enough to do that kind of stuff (my docu work hasn't been very good at all). Also, I only have one camera at present, and while a talented person could do it with one camera, it's not really fair to the bride and groom to limit them to only that.
I'm mainly still learning, but having so much fun doing it. If I could, I would do this as a living, but the Comp. Eng. thing is my 'backup plan.'
I'd just like to say, this is a really cool question to find out what people specifically do. I think, though, that no matter what kind of video you do, as long as you enjoy doing it and are respectful of the people/places you are filming, then it's great. And it's also really cool how forums like this allow us videographers to get together and collaborate to make the artform better and increase what we are all capable of. Excellent question, ARichards, and excellent forum, Videomaker!