I meant to include this in the previous post but forgot.
Another interesting thing is that being on immune suppression drugs after having an organ transplant drastically raises the chances of developing some (but not all) cancers. In particular, we see the sort of cancers that are a product of chronic viral infection and genomic irritation. Squamous cell carcinomas of the skin are a big one. Women can get these in their cervix from HPV; immune suppression makes everyone all the more vulnerable to HPV. Other viruses, like Epstein-Barr that healthy people will clear without a problem, will fester in the body and provoke the development of lymphomas and the like.
The fact that some cancers appear in light of a weakened immune system but not others is a useful demonstration of the fact that we really don't know what causes cancer in every case. Sometimes it seems environmental; enough radiation and anyone will get cancer; smoking cigarettes can cause lung cancer too. Cancer can be caused by infection: transplant patients get lymphomas and squamous cell carcinoma; AIDs patients get characteristic neoplasia (cancer) as well. Genetic deficiency of appropriate anti-cancer genes (BRCA mutation, hereditary adenopolyposis coli, other familial cancers) can be a cause. Maybe bad luck has something to do with it too.