I want to use images of various famous people (notably Walt Disney,
Bill Gates, and Timothy Leary) for a parody web site promoting an
original musical currently in production. Where (if anywhere) can I
find photos of these individuals that are public domain?  I don't
trust the various sites that say "as far as we know these images are
public domain..."

You should be aware that even if the image itself is copyright free,
the individuals may enforce "personality rights" or
"celebrity-likeness law" if an image of them is used without their
consent.

http://www.law.ed.ac.uk/ahrb/personality/uk.htm
http://www.hllaw.com/a_celebrity.html

Owain

Parody may be covered under "fair use" doctrine in the U.S. and
perhaps other countries.

I believe fair use covers the content of satires and parodies that
lampoon public figures, yes.  However, I don't see how that would
cover the use of their likenesses or photos, if those are copyrighted.
 If John Q. Citizen takes a photo of Walt Disney in a public
appearance, can Walt (or his estate) forbid the publication of that
photo?  My impression is "no" since that's the life-blood of the
papparazi.

There is a difference between reportage photograph and using someone's
likeness on a website for commercial promotion. You may be in the
clear, or you may not.

Owain