What occupation allows you to travel to foreign countries to live and work for extended periods of time?

Is there anything besides teaching English to foreigners? I would like to work and live in a South American or European country for an extended period of time. Maybe indefinitely.

There is government work, such as State Department or USAID, these positions usually require master's in International Relations as well as knowledge of languages. If you REALLY know some languages and have extensive knowledge of a region, CIA is always looking for good people. There is also non governmental organizations (NGO's) such as the Red Cross, Doctors without Borders (for medical professionals), Amnesty International (for lawyers who know international law). Peace Corps is also an option (pay sucks though).

Journalism is another option. There are lot's of English/expat newspapers around the world that are usually looking for native English speakers who can write and edit.

Most professions can be brought overseas. It really depends on what your field of expertise is.

A diplomat or course - although naturally this takes a lot of education/experience and ultimately time to build up to this level.

Otherwise you could look at the HQ office of an International company serving a region. e.g. I used to work at the European & Middle-East & Africa HQ of an International Japanese company which served distributors in each country. An account manager does a lot of travel and spends substantial time in the respective countries, although it is more of a roving position than stationary. However, there were also transfers of staff abroad as well.

President of the United States of America

Or if your lazy a Ambassador

You may be able to find a job as a journalist. You can probably do it with any career though, but it will be easier for some than for others. For example, if you had a law degree in one country and then wanted to move to another, you may have to get a new degree if you want to keep being a lawyer. Other jobs it may be easy to switch.

I'm a scientist and I know for us it isn't very difficult to find a job in Europe. There are many labs here who hire foreigners, or you can sometimes work at a lab/institute while being employed by an American university. Right now I'm a grad student at an American university but working at a scientific institute in Switzerland.

Diplomacy.