No. If you have a bachelor's degree, you will probably qualify to teach English abroad. But taking a class to prepare for teaching will be helpful and increase the likelihood you get the job.
ESL means English as a second language and might also be referred to as TESL. This means you would be teaching English to non-native English speakers who live in a country where English is the main language, such as the United Kingdom. TEFL means teaching English as a foreign language and is the term used for teaching English to people in a country where they mainly speak another language. TESOL refers to teaching English to speakers of other languages.
A certificate in TESL or TESOL will qualify you for most teaching jobs. Investigate any course of study to make sure it's legitimate.
You can find an online TESL course for less than $200 as of July 2009. Spend more and have tutor support or take residential training in another country.
While you don't need teaching experience, if you decide to teach English abroad, you will be working as a teacher basically full time. Network with others who've gone this route to learn what's involved before you take the leap.