Careful review of the data suggests that Gardasil is probably as safe as any other vaccine. In fact, it may be even safer, as the reporting rate for adverse events is approximately half that for most vaccines.
Out of more than 12 million doses of distributed vaccine, there have been only slightly more than 7,800 reported adverse events, and the vast majority of those reports to VAERS were for minor conditions, such as injection site pain, which are common to many vaccines. There have, however, been reports of other, more serious, adverse events.
According to the CDC, of 15 deaths reported to the VAERS between 6/8/06 and 4/30/08 as potentially linked to HPV vaccination, 10 were clearly not related after investigation, and 5 didn't provide enough data for a definitive conclusion. Similarly, of the 31 cases of Guillain-Barre Syndrome (GBS), only 10 have been confirmed of which 5 were reported after use of multiple vaccines, and 9 cases are pending. That number of cases of GBS is not inconsistent with the rate of disease seen in the general population, and as such can not be linked definitively to use of Gardasil.
It is important to remember that there are limits to the vaccine adverse events reporting system. In order for researchers to be able to learn about those side effects that are actually related to vaccine use, they must collect every possible bit of data -- and a lot of the reported events will have nothing to do with the vaccine. People get sick, sometimes very sick, and sometimes they get a vaccine in the week or two before they would have been struck down by a serious illness anyway. The only way to figure out which events are related to vaccine use, and which aren't, is careful investigation. So far, that investigation suggests that Gardasil is nothing to worry about. At this point, the potential benefits in reducing deaths and sickness from cervical cancer and discomfort from genital warts more than outweigh the still primarily theoretical risks.
For more information, I also recommend reading this excellent summary from the About.com guide to cervical cancer

