It seems to me that there are four causes so far:
Old Age
Enforced Regeneration
Trauma
Poison
The interesting one is poison. Obviously, regeneration must purge the body of the poison, otherwise he'd keep dying until he ran out of regenerations. So, if he were to die of a fatal, communicable, disease, the same would likely occur. Or would the new body simply be immune to the poison or disease? This could lead to an interesting situation where the Doctor contracts a disease, regenerates, and is subsequently a source of antibodies.
Suppose he died of decapitation or a severe head injury? This is a specific case of trauma, but one still has to wonder how it would effect the next regeneration. It would depend upon the specifics of the regeneration process, of course, but it's possible that the next Doctor could be retarded or at least amnesiac.
This is an interesting train of thought.
The thing is, we found out in Lets Kill Hitler, that there are poisons that WILL stop his ability to regenerate. It was only because River was willing to give him her remaining regenerations that he was able to be saved (without having to regenerate himself I might add).
True. I suppose, like injuries, some poisons are so serious that he can't bounce back.
Also, we've seen the Doctor have a body part cut off, and it grow back, so why not his head (even though I suspect that will cause him to regenerate)?
Well, it would depend on if the head grew a body or the body grew a head.

If the head grows a body, no problem; if the body grows a head, it would be empty. If both happens, then the Doctor has a full-grown infant twin. It would be an interesting twist to use in a story-- maybe not with the Doctor, but with another Time Lord.
Although David Tennant's human twin was not mindless. Did they ever actually explain that?