Here's a big one that I haven't seen mentioned yet: The Bureau of Diplomatic Security at the U.S. Department of State.  They have 1,200 special agents worldwide and no polygraph in the application process.  You can find out more att www.state.gov

A note to those who are crestfallen about their polygraph results:  I took a government polygraph and was told that my results were "inconclusive."  Several months later I got a call saying I had passed and was offered the job.  I decided to turn down the offer in favor of a job with a non-polygraph agency that paid $10,000 less per year.  My sincere advice to anyone who tests as "inconclusive" and is then offered the job is this: DO NOT TAKE THE JOB!!!  The reason is simple: as a new applicant, an agency has no real reason to suspect you of wrongdoing.  However, during the course of your career, there is a potential to be involved in dangerous and complex situations where your could guilt of a wrongdoing could be inferred (incorrectly).  If the polygraph is already stacked against your innate physiology, you will have already supplied the administering agency the "proof" they need to go with their suspicions.

Fed Up Fed,

Do you mean paranoia on my part or the agency's part?  Are you fed up with the polygraph or its detractors.  I don't feel I was being paranoid.  It strikes me as more of a simple deduction.  I would greatly appreciate it if you could add some context and motivation for your comment, as well as any information you might feel could clear up my apparant misconception.