Dwarves could, however, suffer alcoholism. Dwarf refuses to drink water, and will die from dehydration if you don't always have alcohol on hand for him to drink. Since dwarves have a higher tolerance, this doesn't damage the liver, but the dwarf does drink twice as much alcohol (having him drink twice as often would screw with work management, which is already tricky) per sitting. That, to me, seems a very dwarfy form of alcoholism. You could also have the symptoms increase slowly, causing the dwarf to drink more and more alcohol each time, unless friends or the mayor with a good consoler skill intervene, which would reduce the amount of excess booze they drink (but not cure them, since dwarves are alcohol dependent he could never just stop drinking).
A few others:
Arborophobia: fear of plants. Dwarf will only eat meats and cheeses, and runs in panic from fields (plants in barrels cause an unhappy thought, but the dwarf doesn't panic because they're dead). If the dwarf gets unhappy enough (IE: gets unhappy enough to go insane while already suffering arborophobia), he may grab an axe and attack the nearest tree, then the next one, and so on until he dies.
Acrophobia - dwarf faints if he gets next to an "Open Space" tile. He will recover eventually, but will immediately pass out again unless another dwarf carries him down to the hospital. Will also gain an unhappy thought every time he has to use the stairs and won't take "everybody" jobs not on the same z-level he's on. He can remain functional, however, if you keep food, drink, and either a private room or dormitory on the same z-level he works on.
Ailurophobia - fear of cats. Dwarf flees from cats as though they were hostile. A very dwarfy insanity indeed.
Social Anxiety Disorder - dwarf doesn't socialize. As the insanity progresses, the dwarf gains stronger and stronger unhappy thoughts every time another dwarf tries to talk to him ("Was judged by another dwarf recently"). A good friend with a high consoler skill can reduce the disorder, but it can't be cured.