I'm applying to the JET program this year. Here's the official website for it if you're interested:
http://www.us.emb-japan.go.jp/JETProgram/homepage.html
I have a degree in Music Ed & performance, but I want to travel while I can. My one close friend is in Japan teaching English right now. He didn't make the jet program (even though he knew a bit of Japanese which is a +) so he went with a private contractor which was also hiring, but paid less. The job he's doing is different then the JET program though. He's teaching a group of students privately, whereas in a the JET program you're an assistant to an English teacher in school.
But be warned, if you're thinking of applying this year (to start working August next year) you need to turn in a ton of shit by the deadline on December 4th. I think the thing that takes the longest is getting a passport, so work on that immediately if you intend to do this for next year. You'll also need two letters of recommendation, proof that you're going to graduation in time if you don't have a degree yet, etc etc, it's all listed on the website for ya.
Jam it back in, in the dark.