It seems to me that there are four causes so far:
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.
Another interesting scenario would be if he died of cancer (can Time Lords have cancer?). How would the regeneration effect the cancer cells? All sorts of possibilities present themselves here, the most obvious being a sort of evil twin, a personification of the cancer.
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.