There are many companies and organizations that offer opportunities to teach English abroad. Be sure to read the fine print (a small placement fee is not uncommon, but shy away from programs that charge more than that. When in doubt, consult with Fellowships Advising). The opportunities below are primarily government-supported initiatives that offer some sort of stipend.
Austria: US Teaching Assistantships in Austria
France: Teaching Assistantship Program in France
Georgia: Teach and Learn in Georgia
Hong Kong: Hong Kong Native-speaking English Teacher (NET) Scheme
Japan: Japan Exchange & Teaching Program for US Citizens (JET)
Multi-country: Fulbright English Teaching Assistantship
Multi-country: CIEE Teach English Abroad (this is not a government-supported program, but some Temple alumni have worked with them)
South Korea: English Program in Korea (EPIK)
Spain: North American Language & Culture Assistants in Spain (other programs that Temple alumni have participated on include Meddeas and Beda)
Taiwan: Taiwan Foreign English Teacher Program (NOTE: Most applicants will apply to their Foreign English Teacher Assistant program. Be sure to scroll down to find out about this program,)
Thailand: Teach Thailand Corps (TTC)