If I place a regular expression in robots.txt will it be readable for the web crawlers?
No, the robots.txt syntax only supports wildcards, and not regular expressions. See here for a good discussion of the syntax: http://www.robotstxt.org/robotstxt.html.
While it's not part of the standard robots.txt protocol (and therefore not globally recognized), Google and Bing both support LIMITED pattern matching.
Will block Googlebot from any directory beginning with "private". Currently, Googlebot supports
Details on Googlebot's pattern matching: http://www.google.com/support/webmasters/bin/answer.py?hl=en&answer=156449