I got the first shot in the Gardasil series as an adult, even though I already had/have a strain of HPV (one of the cancer-causing strains, which has been fun). I was forced into it as an adult by a nasty, inconsiderate, rude, dismissive, intimidating doctor. I threw up and felt weak & dizzy before ever leaving the office. I never went back for the subsequent shots; I was in a monogamous relationship with my now-husband and, as I said, already had (at least) one strain of HPV; and after how I felt after the first shot, I wasn't going back for more.
I am still battling the cervical issues that have come up due to the HPV. I've had numerous pap smears and cervical biopsies, as well as a LEEP procedure (this is where they literally cut & burn away a chunk of your cervix). The LEEP did not end with clear margins so my pap smears still come back "bad" and I've been urged to have more cervical biopsies and likely LEEP procedures, which I'm really just not interested in. I firmly believe that I have PTSD due to the trauma of everything that went on, including the procedures themselves and the doctors who performed them. I have yet to meet a gyn who understands how absolutely disgusting and invasive I find these procedures to be and understands the mental toll they take on me. (/ side rant)
All of that said, I don't think that I could in good conscience let my (hypothetical) daughter receive this vaccine. I got sick from it, but entirely too many other girls and women have gotten way sicker from it. This vaccine was released prematurely and needed more testing. I want to see what the long-term results are when all of the 12-year-old girls who are getting it now grow up and try to reproduce, etc. I'm not an anti-vaxxer by any means; my future hypothetical children will definitely be vaccinated against polio, mumps, rubella, measles, whooping cough, chicken pox, etc. But I don't think this HPV vaccine is a good idea right now. And I say that as someone with HPV and who has had a lot of trauma relating to it.