Actually, there is ONE that I would recommend. The first one that I thought of doesn’t connect to schools in South Korea. However, if you’re qualified (Bachelor’s degree and TESL certificate with supervised teaching practice) they have excellent schools (no crappy chain school selling school-made textbooks to students for $100 or anything like that). This one is International House, and they are an affiliation of high-class language schools around the world. They have schools in Vietnam, Malaysia and China if you’re keen on those countries. See the first link.

The second company, which does connect you to schools in South Korea, is called Footprints Recruiting. They have year-round placements in Korea requiring only a Bachelor’s degree (not TESL certificate). If you complete the one-year contract you will get your airfare reimbursed, and most contracts include accomodation.