I suspect that a potential employer did a background check on me
without my knowledge.  Is there a way I can get information on what
companies or entities did a background check on me?  Specifically, is
there a service I can pay for that would list the companies that have
done investigative background checks (credit reports, criminal
background checks) in the last year or so?

Credit reports-yes. Check with the credit reporting agencies. There
are 3 big ones:  Experian, Equifax, and Trans Union.
http://www.experian.com
http://www.equifax.com
http://www.transunion.com

The last credit report I saw showed everyone who checked.

I doubt that you can find out whether someone has done a criminal
background check on you, but perhaps someone else knows better.

Welcome to the internet.

They might have but they can legally. Most items are now public
record... I could run a background check on you without your knowledge
and this is legal.

I do not want your name but what state, city and county do you live in?

If it is a fairly decent size city I could send you sites that will
let me pull your information up free of charge.

Thanks
Steve