We should be highly skeptical of them.
But let me back up.
I'll get into why the science doesn't align with the reports you mentioned in a second. But first, I want you to keep something in mind. Politicians are not scientists. The Advisory Committee on Immunization Practices (ACIP), on the other hand, is the panel of experts that decides what vaccines will be recommended for the routine schedule, and they do so based on all available scientific evidence that shows the vaccine to be safe, effective, and necessary. If policy makers decide to require that all 7th graders have their meningitis vaccine, but not the HPV vaccine, it doesn't mean that the meningitis vaccine is more important or safer -- it means that the policy makers decided it was. Scientists should determine what vaccines should be recommended, not politicians.
That being said, let's look at what the evidence says.
The HPV vaccine is at least as safe, if not safer, than the other recommended vaccines in use today in the U.S. Is it 100% safe? Of course not. No medical intervention is. And anybody demanding (or offering) absolute guarantees doesn't understand medicine. Because like it or not, all medical interventions have risks. There will always be someone who is allergic to something or doesn't respond properly or who has something going on that we don't know about. Medicine is not one-fits-all, and so there will be risks for some people. The big question is: do the benefits outweigh those risks?
And here is what we know about the risks associated with the HPV vaccine:
As of Spring 2013, more than 56 million doses of HPV vaccine have been administered in the United States. HPV4 (brand name: Gardasil) accounts for 99% of those doses , so I'll focus on that particular vaccine.
We have a number of ways to track vaccine safety after it comes out on the market. One of those is the Vaccine Adverse Event Reporting System (VAERS). Something important to note here: Anyone can report any reaction following a vaccine dose -- even if they aren't sure that the vaccine caused the adverse event.
Number of serious and nonserious reports of adverse events after administration of quadrivalent human papillomavirus (HPV4) vaccine in females, by year -- Vaccine Adverse Event Reporting System, United States, June 2006-March 2013*
What this graph says is that between June 2006 and March 2013, there were a total of 21,194 adverse events reported to VAERS following a dose of HPV4. Does this mean that the HPV vaccine caused those 21,194 events? No. All it means is that those events happened after the vaccine was given.
This is where Jae Won Joh's point about correlation not equaling causation comes into play. If someone eats a peanut butter sandwich and then drives to work and gets into a car accident, does that mean that peanut butter sandwiches cause car crashes? Of course not. Just because something happens right after something else, it doesn't necessarily mean they had anything to do with each other.
So when you see that "1,968 adverse cases have been presented to the Japanese government, detailing severe medical side effects" , you have to take it at face-value. Lots of people suffer from a wide range of medical issues every day. What's important to find out is: were those medical issues actually caused by the vaccine, or are they just coincidental? You can't get that from reports alone.
These reporting systems are important, however, because they help scientists identify potential reactions that were too rare to spot during pre-licensing clinical trials. If we see enough reports of the same reaction, scientists do the research to see if those who received the vaccine have a greater risk of that happening than those who didn't.
And that's what we did.
The Vaccine Safety Datalink (VSD) analyzed specific adverse events -- like Guillain-Barre syndome (GBS), stroke, seizures, and severe allergic reactions -- following more than 600,000 doses of HPV4. They then compared the rates of those events to a population that didn't receive the HPV4 vaccine. They found that none of these severe reactions were any more common in those who got the vaccine than those who didn't. 
Other reports that the HPV vaccine has caused infertility (as the Japanese news articles have suggested), blood clots, autoimmune disorders, or death have all been examined, too. And there is no evidence that the HPV vaccine caused any of those serious reports. [5, 6, 7, 8]
What is probably caused by the vaccine are the same temporary side effects that we see with all vaccines in that age group:
- fainting (adolescents faint a lot during any medical procedure)
- fever (1 in 10 people will get a mild fever, 1 in 60 a moderate one)
- pain and redness a the injection site
The worst that almost all people receiving the HPV vaccine can expect is feeling a little icky for a day or two.
The vaccine is so safe partly because of how it is made. The HPV vaccine is a recombinant vaccine, which means that it's made by taking virus-like proteins that are manufactured using yeast cells . We don't use the whole virus, like we do in some other more widely accepted vaccines. In fact, it's the same technology that we use to make the Hepatitis B vaccine, which is recommended for babies on the day they are born. If the HPV vaccine were given at a younger age with the majority of the other vaccines, I wonder if we would even be having this debate right now.
Something else to note about that graph is that you'll see the number of reports have gone down despite vaccination coverage going up. Given that the vaccine hasn't changed, it's likely that the reports were caused more by fear and hype than the vaccine itself.
So those are the risks, what are the benefits of the vaccine?
Almost all adults will get HPV at some point in their lifetime -- often very shortly after their first sexual experience. But just because it's transmitted sexually doesn't mean that it only affects the sexually promiscuous. Penetration is not necessary. Anybody with fingers, a mouth, and genitals can get and spread HPV. Even virgins can get HPV. And when 80%+ of people get it, it's normal. It's part of every day life, like the staph on our skin or cold sores. Very few people can say "that I/my child won't get HPV" and mean it. Almost everybody gets HPV.
Thankfully, most people clear the infection with no problem. Some infections, however, can lead to a variety of cancers (see the table below). In fact HPV is estimated to cause 26,200 cancers every year in the United States , and 5% of all cancers worldwide .
Both HPV vaccines protect against the two-types of HPV that are most commonly associated with these cancers, and are credited for cutting the incidence of these HPV types in half. This is despite a really low coverage rate (less than half of all U.S. adolescents have received the full vaccination series) . It's a highly effective vaccine. And while it's too early to have direct proof that it reduces cancer (that will take years), we know the vaccine reduces the HPV types that lead to most HPV-related cancers, as well as pre-cancerous lesions .
And in exchange for reducing our risk of a variety of cancers, the vast, vast majority of us face only having fever or pain and swelling at the injection site.
We have a vaccine against cancer. Let's have a large-scale conversation about that.