All of my experience has been in finding teaching positions, so most of the information is geared towards that. However, you can use the links at the end of this post to find a great variety of different careers, some with no language requirements at all. Check them out.
In the future we'll go into more detail of how exactly to approach applying for a job, give a rundown of the different companies and advise on other career choices.
Use these links to find Instructor positions in Japan. Some are in school, such as JET and Interac, but most are eikaiwa (English conversation schools).
iShareJapan has a great list of Eikaiwa schools in Japan.
Local government jobs are very desirable and will pay about the same or a bit more than the JET program. They are pretty hard to find, though, and competition can be tough. Most successful applicants already live/are in Japan, and more often than not speak a decent level of Japanese. Use the job websites listed below to find this kind of job.
Many smaller schools advertise online for English teachers. Beware that a lot of the part-time or pay-by-hour options can lack security or may not pay a livable wage if you're living alone. Here are some links to investigate by yourself:
The above links also have many other types of jobs in various sectors. Beware: don't look if you aren't qualified, because they pay a lot more than us lowly teachers get!
And that's about all we have for you for now. If you have any experience using these job sites, or know anything we've missed here (or would just like more information), post us a comment in the box below the related posts.