I ran a quick search through the DF suggestions and I didn't notice anything about diseases that spread like the cold and flu. This idea seems like if it was poorly executed it could be more annoying then interesting, but it might be a bit of fun.
I was thinking something along the lines dwarves that contract the disease (either randomly or through contact with dwarves that have it) will have a few days of incubation, then find themselves feeling ill and retire to bed (maybe only doing very important jobs, i.e. operating a catapult or pulling a nearby lever). Maybe the symptoms could be randomly generated for added fun. Doctors could diagnose patients and if serious enough administer aid. Perhaps dorfs could even have a personality trait that makes them either not care about sickness (Continue working through it, unless told to rest) or hypochondriac dorfs who will retire to bed if they even hear about illness.
The main problems I foresee is how a well timed epidemic could wreck a fort against invaders, which is why I think that the symptoms should be rather small, and not every dwarf contacted should contract the illness. Depending on if hygiene is ever implemented, particularly dirty and blood-spattered forts might attract diseases of greater and more dangerous magnitude, like a real bubonic plague. Or maybe an elf would give a dwarf a disease, and their hippy-itis might have a more acute affect because it's a cross species transfer, the possibilities are endless
As a final note, I would like to bring up one more point.
Forgotten Beasts composed of disease, or belch out contagious epidemics.
Painful, painful epidemics.