When capsicum comes in contact with the skin it causes an increase of blood circulation to the area, which is one reason it has been used to help treat ulcers and heal wounds. When Hannibal crossed the Alps with his army, they sprinkled capsicum into their boots to increase circulation and stop their feet from freezing.
According to my herb books: Capsaicin fights cancer by preventing carcinogens from binding to DNA, "where they trigger processes that cause lung and other cancers". This doesn't mean chiles are a cancer treatment, but can help to reduce the risk of certain types of cancer.
However.... the following snippit has a section in bold that explains the cancer info and capsium.
snip
There is a special neurotransmitter in our nerves which transmits signals of pain, so it is called substance P. It has been found that the capsaicin of capsicum depletes the nerves of substance P, thus greatly reducing signals of pain. That is why capsium was used as an old remedy for toothache and in painful injuries. Another modem discovery is that while capsaicin causes a local burning sensation, it stimulates the brain to release endorphins in the brain. Endorphins, create a feeling of great well-being. At least one authority believes this explains why some people seem addicted to eating hot peppers, they are addicted to the endorphin high it gives them.
Several medical studies have shown that capsicum increases the level of fibrinolytic factors in the blood very rapidly. Fibrinolytic factors dissolve blood clots. This effect is very rapid, but subsides within another 30 minutes. However, when taken on a daily basis, there is a gradual build-up of the fibrinolytic factors in the blood.
Another marvelous effect of capsicum on the blood is its ability to lower triglycerides and cholesterol. When capsicum is fed with a high cholesterol meal, only a moderate amount of the cholesterol is absorbed in the blood stream and a large amount passes out unabsorbed with the feces. At least one research team has reported that capsicum has a beneficial effect on lowering the systemic blood pressure.
Large amounts of capsicum ingested on a daily basis has been shown to be associated with an increased risk of cancer, while the daily intake of small amounts of capsicum is associated with a lower incidence of cancer.
A large dose of capsicum on the day of a highly stressful activity has been shown to increase stamina, however a large dose taken for three days prior to the stressful event did not produce an increase in stamina. It is clear that moderate daily doses of capsicum may be beneficial while large doses should be reserved for occasional use when required.
http://www.your-health.com/capsicum.htm
I don't have time to do a serious search but here's one:
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=12208187&query_hl=3&itool=pubmed_DocSum
It's entirely possible that it promotes some types of cancers (i.e. of the upper digestive tract) and inhibits others (after it is partially digested into different compounds by the high acidity of the stomach and/or by the liver). Aspirin is like that -- preventive effect on colon cancer, but promotes pancreatic cancer (it's generally recommended because colon cancer is far more common than pancreatic cancer, but people with a family history or other risk factors for pancreatic cancers are being advised that it could have a bad net effect on their risk of either cancer).
The capsicum family includes a variety of plants, including sweet peppers, which produce different capsaicinoid compounds which have different effects (I don't think research is very advanced on any of them, but I'm sure that's about to change re capsaicin at least). It's entirely possible that most have only a beneficial effect, and that capsaicin quickly converts into something more like the others (i.e. losing the feature which causes the burning effect while retaining other beneficial features).
This link is to an abstract re capsiate, a non-burning capsaicinoid found in sweet peppers, and its anti-cancer properties.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=12594536&query_hl=7&itool=pubmed_docsum