Is it possible to find a job overseas for only a few months?
For a few years?
For the rest of my life?

Yes!

Short-Term Jobs

Job opportunities for short-term employment can be quite limited in most occupations.

In many countries there are considerable costs, in terms of money as well as in time and headaches, to obtain legal residence visas and work permits for employees.  Therefore, you will find a smaller pool of employers who wish to employ you. 

If you are flexible and would consider teaching English - in the last few years more and more short-term positions have become 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. 

If English isn't your thing - TEFL Temp has a page on volunteer programs that are often looking for people with other skills.

One Year - or a Life Time - Overseas

One-year jobs are relatively easy to find and if you wish to spend the rest of your life working 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 teaching English overseas at about the age of 40 - and had no problem at that time either. 

As always, your specific skills and education will play an important role.  But, generally speaking, if you have a degree  and some training in teaching English - you work almost anywhere, at almost any age.