The leading choice for contraception in Japan is condoms, the second most popular (almost 20%) being pulling out, followed by the rythm method. The pill languishes in last place with an audience of just over 2% of the female population (vs. 18% in the US, 25% in the UK and 52% in Germany, for example).
- The Pill
There are strict rules on bringing the pill into the country. It must be prescribed to you, and you're only allowed two months' supply. My girlfriend tried to bring more than that and had her parcel got stopped at customs waiting for her permission to destroy the contents. They wouldn't even send it back to England.
You can get prescribed it here by an obstetrician and it costs about 3000yen per month, and you have to go back every three months for a check-up (not free).
I recently found a great article about the types of Pill available in Japan. - Depo-provera is not permitted.
You can't bring it with you, and no-one will import it or inject you with it even with a prescription. However, there are similar shots available. Ask a gynecologist. - Contraception patches
There are several types of estrogen-only patches available (on insurance). - Gels
Several types containing both progestogen and estrogen. - Condoms
Japanese condoms are okay, but (it's not a joke) they will not always fit Western men comfortably. They may also come off more easily than what you're used to. There are several shops in the big cities that sell all sizes and shapes. Look for The Condom Store, Condomania or places like that. - The morning-after pill
Is very expensive (10,000yen and up) and not covered by health insurance, though I have heard of it going for only 3,000yen in Okinawa. It's referred to as the "aafutaa piru" and you need to see a gynecologist to get one. International clinics will also prescribe it to you if necessary.

How could the pill increase the risk of HIV/STDs in a country where the preferred methods of contraception are withdrawal and rhythm method?
Logically it makes no sense. And, I assure you from extensive experience (/extensive/ experience), Japanese men do not willingly use condoms.
When I lived in Japan, I brought 6 months of pill on my person (scattered around my numerous bags) and had my family periodically send me care packages that included 2-3 packs of contraceptives. I lucked out in that I never got stopped at Customs, and my packages were never held.
But, especially with hormones, you can't fuck around and just switch to another type. The dosages for Japanese medications are based on the average weight of a Japanese woman - which is 5 to 7 kilos smaller than the average for a Western woman - and the chemical composition of the synthetic hormone itself varies with every single brand of pill.
For women who will be in japan for the long term, I recommend you consider an IUD. It offers up to 5 years of protection, and there are both hormonal AND non-hormonal options available. There are also the Norplant/Implanon/etc. implants which also offer long-term protection. Both the IUD and implant have GREAT effectiveness rates and you can't "misuse" them. They also have fewer side effects than Depo Provera, though they carry their own risks, too - e.g. if you catch an STD while on an IUD you are at high risk for PID (due to the fact that our cervix kind of remain open).
Nonetheless, USE CONDOMS. I reiterate, USE CONDOMS when engaging in sexual activities with anybody, but especially Japanese men. They like to pretend that STDs are a "gaijin's disease" but it's not the case, and the way they ignore the reality of STDs and especially HIV (HIV testing is not encouraged and anti-retrovirals are not covered by Japanese health insurance as they are considered "preventative") means the number of carriers, especially middle-aged men who often patronize prostitutes in Japan and abroad, is much higher than the populace and gov't want to admit. They don't get regular screenings - just try to ask your partner to get an STD panel, he'll brush it off completely or take offense and assume that /you/ have something. I once asked a guy the last time he got tested, and he told me "Oh, don't worry. The last girl I slept with, my best friend slept with her afterwards, and he didn't catch anything, so I know I'm clean too." :|
So, I recommend an IUD or implant to aid in pregnancy prevention and to regulate your menstrual cycle, but do not - I repeat, again - DO NOT FOREGO CONDOMS. Remember that children are not the only thing you can "catch" but they are the most curable. Always practice safe sex - at home, but ESPECIALLY abroad.
If you can't go on an IUD or implant for whatever reason, I still recommend the pill - and stick to the pill you are used to. Whether or not you plan to be sexually active, I strongly, STRONGLY encourage you to also bring a pack or a few packs of EBC from home (or have the mailed one pack at a time to avoid customs issues). You never know what will happen, and you DON'T want to be caught without EBC when you need it, especially if you have to jump through hoops to get it. Remember, EBC is only effective if taken within 72 hours of unprotected sex.