Do cockroaches have less health issues than humans?
AndroidPenguin, where did you read that our immune systems are far better than those of 'a cockroach'? This seems pretty strange to me, but I'd be interested in reading a study that compared human and cockroach immune systems if you can provide a reference. 

Victor, with respect to cockroaches, there are numerous species of cockroaches. Here's a page about cockroaches with a link to publications on cockroaches and a phylogenetic tree of the families and subfamilies. 

http://www.bio.umass.edu/biology/kunkel/cockroach.html 

All those species tend to occupy distinct niches with distinct traits. With respect to cockroach evolution, sewers are too new a phenomenon to have had an influence on cockroaches. Rather cockroaches have been successful in adapting to this novel 'habitat'. The same holds for rats and other denizens of sewers. Sewers are a very nutrient rich environment, and as in many nutrient rich environments, a few species tend to possess the right traits (whatever those may be) to survive and out-compete other species. To take an example from coral reefs, when coral reefs suffer from eutrophication, this leads to a growth in phytoplankton and a reduction of the euphotic zone that can lead to the death of all but the most resistant corals. Likewise in the terrestrial environment, only the most tolerant or opportunistic species tend to survive in highly perturbed and nutrient rich environments like sewers. With respect to cockroaches getting cancer, I've never read anything about insect cancer, but I imagine in theory that they could get cancer. I'm not sure, however, of the impact given the much shorter life spans of insects. It's an interesting question though.