I guess you all know those "one image per day" timelapses, e.g. http://www.youtube.com/watch?v=6B26asyGKDo&feature=related. Has anyone experience with that? I want to that for let's say one year, with the same background (white wall). How can I set up the camera for that to have a stable series?

I have done a couple of variations on that theme. The biggest hassle is getting your head in exactly the same position and at the same angle relative to the camera. It is very easy to have your chin slightly lower or higher with your eyes still fixed on the camera, which can give a completely different look.
If you use a flash and a fixed camera position it is easy enough to get the lighting roughly the same.

For this one from a couple of years ago I went through and centered the images on one eye in post...
(The ice build-up looks much better in the hi-def original)

If you don't have the room to keep dedicated tripod in the same spot for a year you can always fix it in post. You can either stack the photos in Photoshop and align that way or create a layer with some sort of mark where you want the center to be (ex. eyes or mouth) and then align that way. 365 photos is not that much to manually edit.