Here is one of my customers, performing some action after having logged in to his account. The unique token is simply an encrypted user id + timestamp.
94.254.xxx.xxx - - [02/Jul/2011:22:25:46 +0200] "GET /some-action/unique-token-123abc HTTP/1.1" 200 410 "-" "Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; Trident/5.0)"
Now, Googlebot somehow found out about this unique link and tried to access the exact same URL one week later.
126.96.36.199 - - [10/Jul/2011:09:56:01 +0200] "GET /some-action/unique-token-123abc HTTP/1.1" 302 - "-" "Mozilla/5.0 (compatible; Googlebot/2.1; +http://www.google.com/bot.html)"
(status code is 302 because the token had expired)
Let me emphasize that this is a unique URL that was visible exactly once, for only 2 seconds, before the user clicked it and proceeded to visit that page. It was not sent in an email or published anywhere public.
What is going on here, how is it possible that Google found this unique URL?