1. Pension (ペンション)Pensions are Japanese Bed & Breakfast that usually offer dinner in addition to breakfast with your stay. They're modeled after the pensions of Europe. Rooms are generally western style.
Like, Bed & Breakfast pensions are usually small family run businesses. It's common to get to know the proprietors and other guests. Japan has hundreds of pension style lodgings. Each is unique.
2. MinshukuMinshuku (民宿) are much the same as pensions except that they have Japanese style rooms and meals. In many ways, they can be considered budget versions of ryokan.
In many cases, pension are more elaborate than minshuku. It's expensive to build a large western style house in Japan. The owners of pension are often well off. Minshuku are sometimes a family home with a few spare bedrooms.
3. Temple Lodging (Shukubo ~ 宿坊)Long before the first Japanese hotel was constructed in the Edo-era Japanese travelers knocked on the door of a temple whenever they needed somewhere to stay.
This tradition continues to this day — temple lodging in Japan is a recommended cultural experience.
Temple lodging isn't for everyone. Walls in temples are thin — it's not a great place for young families or party people. Expect significant culture shock. Breakfast and dinner may be included with your stay. Food is always traditional Japanese Buddhist vegetarian food (Shojin Ryori).
4. Business HotelsJapanese business hotels offer spartan accommodations in convenient locations at reasonable prices. They focus on traveling Japanese salary men who just need somewhere to crash when they're on business.
5. Capsule HotelsCapsule hotels are a product of the 1980s and 90s. They're a good low budget option for single travelers. Couples can't stay together (or even on the same floor) in a capsule hotel.
Capsule hotels are surprisingly comfortable. They also represent a unique experience for the adventurous.
6. Youth HostelsJapanese youth hostels are much the same as the youth hostels of Europe except that rooms may be Japanese style.
7. Karaoke and Manga CafesSome budget travelers may be tempted to spend their vacation sleeping in karaoke or manga cafes. These aren't viable options. There are people living in manga cafes in Japan — it's a form of homelessness.
As a visitor to Japan it's important that you secure reservations for the entirety of your stay. You'll be lost enough without wondering where you're going to sleep each night. That being said, if you miss your last train and are facing an expensive taxi ride home — staying in a manga cafe for a few hours is a viable option.
Japanese salary men crash in an manga cafe when they miss their last train. University students do the same.