Something said in Fortress Mode set me to thinking about how currently, the only way to die that isn't a direct result of enemy action, bad luck or player intervention is generic "old age" that happens more or less at random.
Disease has come up a time or two before, and would seem to be the easiest one to implement. Just give miasma and tainted water various appropriate syndromes, preferably with a disease-resistance attribute check, and some sort of mechanism for the effects to be communicable: Coating every afflicted dwarf in some sort of invisible syndrome-causing substance, perhaps? You could even be really hardcore and give mud a weak syndrome effect with various minor symptoms, to represent the minor ailments caused by inadequate hygeine facilities, or give snow a syndrome to correspond with pneumonia; I got the impresion from that comment about setting the wagon on fire and melting all the badgers that the rains of various unpleasant substances are going to have syndromes of some kind, so this should be a simple enough extension of that concept.
Stuff like heart attacks or strokes would be a bit more difficult, but the easiest way would probably be to add a variety of prone-to-failure stat for each major organ that decreases by age and genetics. The main use for this would be to keep fortress populations at a sufficiently high turnover that FPS and food, booze and living-space requirements never get totally out of hand no matter how long your fortress lasts. Of course, it would be vitally important to modify the thought system so that the death of a dwarf from natural causes at a great age didn't cause as severe an unhappy thought in all their friends and family as from contaminated drinking water or a Hammering for not fulfilling a mandate.