Cancer - I think it's unlikely because of the complete nature of the shift and probable hyper-immune systems. I would believe it if someone told me that there were very rare (or even only werewolf-specific) forms of cancer that we *could* get, but since we basically do a whole reset down to the DNA every time we change, it would have to be a rare unfortunate thing indeed.
Most bacteria and viruses - we're presuming unlikely, because, again, improved immune systems. Plus, the molecular and cellular-levels alteration in the change would stop most pathogens dead in their tracks.
Parasites - this is icky, and frankly I'm having trouble thinking of a mechanism for lycanthropy that would deal with parasites. Unless the intrinsic proteins in our blood caused them to just die on their own - I'm not going to call "super immune-system" on this one, specifically because parasites are dealt with by IgE, and an excess of IgE = asthma/eczema/hayfever trilogy, sometimes to fatal levels (ask any major asthma sufferer). So if we had super IgE, we'd probably all die of asthmatic reactions to our own fur. Otherwise, I'm pretty sure that the stress of the change wouldn't make much difference to a tapeworm. If there's someone out there who can think of a mechanism by which werewolves can be immune to parasitic infections...which anyone who eats fresh prey is just asking for, be they cats, wolves, or H. alleged-sap....I'm dead curious to hear it. Until then, I might just check in at my vet and tell him that my large dog has worms again a little more regularly (it's the same medication for canids and monkeys).
Silver poisoning, regeneration, and other favourite tropes: buyer's choice, really. Many interesting and acceptably plausible explanations have been put forwards for all of these.
Any other medical people out there who would like to explore the fascinating intricacies of possibly being a pack doctor with me?