Thanks for writing in. Vasectomy is a solution for permanent contraception for men. It involves closure of tubes which carry sperm from testicles to the ejaculatory duct. It does not affect the testes or sexual ability in the operated individual.
There are no studies that support an increase in prostrate cancer after vasectomy.
I respectfully disagree with Dr Veena's answer. There are at least four different studies that I know of that show "irreversible testicular fibrosis" (scarring) in all mammallian subjects
Doctors state that this does not affect testosterone production but I and several other men I am in contact with disagree. At 38 my testosterone dropped 38 % in a few months and I am now on testosterone gel (probably for life).
As for cancer, well that is still being debated as well. This from Campbells Urology, Considered the "Bible of Urology"
"A relationship between vasectomy and prostate cancer risk was initially suggested in 1993 with a relative risk of 1.6 based on two large cohort studies (Giovannucci et al, 1993a, 1993b  ). Risk increased with time, so that men who underwent vasectomy at an early age had a higher risk. A recent meta-analysis reported a pooled risk of 1.37, with a linear trend suggesting a 10% increase for each additional 10 years since vasectomy ( Dennis et al, 2002a ). The biologic mechanism by which vasectomy might predispose to cancer is unknown, although presence of antisperm antibodies and decreased seminal androgen concentrations or secretory activity have been proposed. The magnitude of the relative risk is small enough to potentially be explained by ascertainment bias because men who have undergone vasectomy may be more likely to seek follow-up with a urologist."
You will also be told that ejaculation and orgasm are not affected but for me and numerous men I have spoken to this has not been the case. My sex life was killed by vasectomy at 38 and it its place I got pain.
As I am typing this I am sitting in my bed recovering from my second surgery (vasectomy reversal) in an effort to stop the pain caused by this "simple procedure." I do not know if I will ever get the good sensations back. Had Urologists told me everything (such as the info above) I probably would not have gone through with it. I was misled (It appears to be accepted industry behavior) and now suffer.