It entirely depends on the country and each country has different qualifications. It can be more expensive, but in most countries it's advantageous to be in the actual country to find a job. That will give you some advantage over others since you can interview with the school in person versus over the phone. That's also a good way to get a good ESL job.
Depending on the school and the country schools can sometimes save money by hiring teachers in-country versus hiring a teacher from abroad, such as in Korea where they won't have to pay your plane ticket if you are already there.
Here's the deal in a few Asian countries.
China
Some schools here will hire foreign teachers from abroad. For these check ESL Cafe and for jobs for those already in China you can check Echinacities.
Japan
A few of the bigger chains will hire teachers from abroad. These are private schools like AEON, GEOS, ECC and AMITY. The JET program and Interac which place teachers in public schools also hire from abroad. So there are a number of schools and programs that will hire from abroad. For these you can check sites like ESL Cafe. However, there are more jobs available if you are already in Japan and on other sites. For these you can check Ohayo Sensei or Gaijin Pot.
Korea
Many public and private schools hire from abroad and this is usually a good place to get hired from abroad as most schools will pay your airfare upfront. A good place to find a job in Korea while in your home country is at ESL Cafe. If you are already in Korea you might want to check Koreabridge for jobs.
Teaching in Korea also requires some additional documentation.
Taiwan
Jobs are rarely advertised abroad on such sites as ESL Cafe. Hess does some hiring from abroad. For the most part you'll have to get to Taiwan first. You'll find many jobs on sites like Tealit. If you are not already in Taiwan I wouldn't bother looking for a job there as most schools will ignore you and take from the pool of teachers already there.
You might also be interested in reading about how I got a job in Taiwan.
Saudi Arabia, UAE, Dubai
If you have good credentials, experience and/or are a licensed teacher then finding a job from abroad here is fairly common. Many schools will pay upfront for your airfare. ESL Cafe is a good place to look for jobs here.
For more information on acquiring the proper visa to teach English or to get started in China, Korea, Taiwan or Japan check out the Ebook. You may also be interested in how to find an easy going job in Asia.