J.B.
Here's what I know...take it FWIW.
The HPV vaccine is supposed to prevent 4 types of HPV that are correlated with certain cancers, including cervical, penile, anal and throat cancers, as well genital warts. There are hundreds of strains of HPV that the vaccine does not cover. Many, many people (estimates are as high as 80%) contract some strain of HPV in their lifetime and most people don't know they have the virus, have no symptoms, and recover completely on their own via the power of their own immune systems in 2 years or less. For the vast majority of people who get HPV, it's a non-issue.
There is no guarantee that someone with HPV will develop cancer, and no guarantee that someone who develops cervical, throat or anal cancer had one of the strains of HPV that the vaccine covers. The strains of HPV that the vaccine covers account for around 70% of cases of cervical cancer and 90% of genital warts - so 30% of cervical cancer cases are NOT from the strains of HPV that the vaccine covers, as well as 10% of genital warts cases. Therefore, it is critically important for even those who have been vaccinated to practice safer sex and get regular examinations (especially PAP smears). Getting the vaccine is not a substitute for good preventative habits and medical care.
For my kids, the answer has been and will continue to be NO to this vaccine. I don't believe that the benefits of this vaccine outweigh the risks. My two oldest are 17 and we have been declining this vaccine for 5 years. I will do the same for my younger boys. They are free to opt to have this when they are 18 and in charge of their own medical decisions but for me, based on the information I have, it's a no.