Is it possible to find a TEFL job for only a few months?  For a few years?  For the rest of my life?
Short- and Long-Term TEFL Employment

Yes!

Short-Term EFL Teaching Jobs

In many countries there are considerable costs, in terms of money as well as in time and headaches, to get their EFL teachers legal residence visas and work permits.  Therefore, you will find a smaller pool of TEFL employers who wish to employ you.  In the last few years though - more and more short-term positions are becoming available.  Some even include airfare.  Head over to TEFL Temp to scout short-term jobs.  If you have trouble finding short-term work (less than one year) in countries where you would like to be located, consider volunteer work - in those same countries.  TEFL Temp has a page on volunteer programs as well.

One Year - or a Life Time in TEFL

One-year TEFL jobs are very easy to find and if you wish to spend the rest of your life teaching EFL around the world - you will find it quite easy to do so.   One caveat is that age discrimination is much more open in most of the world - but as I write this page, I am 56 years of age, with white hair and a wrinkled face.  Yet, I have had not trouble finding good jobs in several countries.  I started in EFL at the age of forty - and had no problem at that time either. 

What about Older EFL Teachers?

Many EFL teachers start teaching English at an older age.  I did.  In Korea last year I saw many teachers in their 40s, 50s and even a few in their 60s.  The same is true in Thailand, Taiwan, and China.  If you are concerned, go on the discussion boards at ELT World and TESALL and ask about the countries in which you are interested. 

Typically, the people who ask get positive responses from older people already teaching there - or who have taught there before.  I recommend these two forums specifically as they are populated by many very experienced "TEFLers" and you'll get better advice than at some of the more popular forums where you are likely to get advice from a newbie in country for only two months . . .
 

Younger EFL Teachers?

Even more demand for them!  Though, you may sometimes find yourself stereotypically slotted for teaching younger students.  They will think that you have the energy that kids require - and schools often worry that younger teachers will not command respect from their adult students.  As the great majority of students at languages in most countries are children - you are all set.