Travel, Teach, Live in Japan
Hi, I don't know how long ago your question was posted, but I thought I'd go ahead try to answer your question.
My husband and I are in a similar situation as you--we're both very interested in Japan, but neither of us have bachelor's degrees. Basically, the short answer to your question is that it is technically possible to find teaching related jobs, etc., without a degree... But the chances of finding legal employment is very, very unlikely. So unlikely, I'd say, that unless you know a Japanese employer personally (and very, very well), it's pretty much impossible. If you're willing to work illegally, on the other hand, I'm sure you could find something... But it would probably make it difficult for you to return to Japan if you got caught at such activities (I have not experiences with this, so I can't say for sure).
The reason for the difficulty of finding jobs is that a Japanese employer has to do more work (and, I believe, pay extra money) to hire somebody that doesn't have a degree. In other words, unless they have a very, very good reason to pick you over somebody with a degree (e.g. if you worked in the entertainment industry and were the more skilled performer), they will definitely pick the degree holding candidate over you.
If you're really interested in Japan, however, (and have some cash/patience) there are other possibilities for getting into the country. Studying Japanese in Japan, for example, allows you to get into Japan with a visa. This would probably be the best way to meet people in Japan who are hiring, since you won't have the option of going through the teaching agencies that many other people use. Being able to communicate in Japanese certainly give a person an advantage over the majority of English speaking foreigners in Japan. Also, if you are studying full time with a student visa, you will be allowed to work in Japan part time whether you have a degree or not. Unfortunately, while studying in Japan isn't necessarily as cost-prohibitive as you might think, to apply for a visa you'll need to be able to show that you have significant funds in the bank--probably much more than you'd actually spend during your studies.
...One thing worth noting about working in Japan with a degree is that any degree--even one in a subject completely unrelated to Japan, English, or anything else in particular--would be completely acceptable. Also, the quality or name of the school you graduate from is unimportant. Therefore, even if you only have an Internet degree in Art History, you're about as qualified, from a Japanese point of view, as a Harvard graduate or an English major.
Well, good luck in whatever you decide to do! If you have any other questions on the subject, I'd be happy to try and help you out.