If you do a web search on "statins cancer," you will come up with a number of web sites claiming that statins may protect against cancer, such as this one: (Statins May Protect Against Cancer) . The study this article referred to was large : it involved 37,248 patients who were taking a statin, and compared them against 25,594 patients who were not. It was noted that, over the course of the study, only 9.4% of those who took the statin drugs developed cancer, as contrasted with 13.2% of those who did not take the drug. The authors provide a caveat, however, that the results are far from conclusive, and offer the following direct quote from Eric Jacobs, the strategic director of pharmacoepidemiology at the American Cancer Society:
"While statins remain important drugs for the prevention of heart disease, they should not be used in the hopes of preventing cancer. Randomized trials have definitively shown that using statins does not reduce cancer risk, at least in the short-term, and most previous observational studies have not found clear evidence that even long-term statin use can protect against cancer," said Jacobs.
Is it the statin drug that reduced the risk of cancer, or rather the highly correlated fact that, statistically, those not prescribed statin had low cholesterol, and were thus more vulnerable to cancer?
In the above study, an especially high benefit was observed for lung cancer and colorectal cancer. There was a well known "Seven Counties Study"  carried out by Ancel Keys in the mid 1980's, before statins were even available by prescription. One clear result revealed by this study was an increased risk for lung cancer as being especially associated with low serum cholesterol levels. A study by Winawer et al. , reported in 1990, also mostly preceded the widespread use of statin drugs. It showed that a decline in cholesterol levels was a predictor of subsequent colon cancer . Thus low or declining cholesterol are risk factors for both lung and colon cancer.
The following website provides a more complete picture by summing up several controlled studies in a single informative chart: (Statins and Cancer: Summary) . The effect of statins on cancer seems to be a complete wash, i.e., only statistically insignificant differences were observed between the statin users and the controls (some up, some down) for several studies included in the chart.
Among the cancers that statin drugs allegedly suppress, prostate cancer is perhaps the poster child. The evidence in epidemiological studies that statins reduce the incidence of prostate cancer seem convincing
(Statins Guard against Prostate Cancer) . Furthermore, a seemingly solid reason for this protective effect is tied to the male sex hormone, testosterone. Testosterone is manufactured in the adrenal glands and the gonads from cholesterol via a biochemical process. These glands don't have to depend on delivery of cholesterol by LDL, as they can even manufacture cholesterol themselves, but this process is also controlled by the very same HMG-CoA reductase enzyme that statins interfere with (Cholesterol and Testosterone Manufacture) . As expected based on biochemistry, the ability of statins to reduce total testosterone has been shown definitively to be true, at least for diabetic men, where the observed reduction on average was from 13.4 nmol/L down to 11.9 nmol/L .
For the past several decades, medical students have been taught in medical school that testosterone "fuels the fire" of prostate cancer. Further positive evidence in favor of statins protecting from prostate cancer comes from the observation that statins appear to lower levels of PSA, a biomarker for prostate cancer that can be measured from blood samples (Statins Lower PSA) .
Of course, arguing this idea is a mixed blessing for Big Pharma, because it means they might have to concede that statin drugs could cause sexual dysfunction. Neither loss in libido nor erectile dysfunction are listed as possible side effects of statin drugs. However, there is plenty of anecdotal evidence on the Web suggesting that they are (Statins and Erectile Dysfunction) .
You may feel that a loss in libido is justified if it leads to a decreased risk of prostate cancer, the second most common cancer diagnosis for men (Prostate Cancer Common) . However, if you want the full story, please read the next section.