This thread has a little discussion on the low occurrence of early death of any kind among hobbits (I believe mostly on the second page).
I believe, not really a "pathogen" per se, but the elves have a sort of sickness of soul that sends them to Mandos or at the least to Valinor as much as anything else (Miriel, Celebrian). I don't think they were susceptible to death by physical illness though.
I don't know a lot about illnesses in other races, but it's an interesting topic.
Sophia