It depends on the disease. They can cause stat loss as olnorton said, but they usually also cause damage. Otyugh strikes will even slow you.
The game is a little inconsistent about what counts as a disease, though. For instance, Dolorous Decay seems like a disease-causing spell, but it only causes poison, not disease. And the damaging effects of Ghoul Lord attacks can be negated with a Cure Disease spell, but the paralyzing effects have to be cured with Remove Paralysis or Free Action.