Some fish are more prone to disease than others, and some have much stricter diet requirements. The reason that most aquarists experience sickness with tangs and angels more often than other fish is because of their inherant delicate nature.
As far as disease resistant fish go, you don't get much tougher than damsels. I have seen damsels live through ammonia levels above 6 ppm for a week. I have seen them be the ONLY fish in the tank not getting infested with Ich. They are tough little buggers.
That said, every fish is capable of getting sick if stressed enough.