Back in 1989, I worked as an English teacher in Taiwan and Korea. I wasn't on any special program--just travelling through Asia, and looking for a way to have a little fun and make a little money. I also don't have any ESL or teaching qualifications--they'll take practically any American that happens by. The pay is low, but a lot of people there are eager to learn English.
I highly recommend Korea. It is a beautiful country, with a lot of great scenery.