If you happen to be using Windows Emacs and Cygwin Python there's an annoying interaction where “M-x run-python” hangs. The easiest way to fix it is to mount the directory where you have your emacs installation into the Cygwin file name structure. For instance, I have my emacs installation in C:\emacs\emacs-22.2, and in a cygwin shell I did mount -b ‘C:\emacs' /emacs, and now running the Cygwin python works.

The emacs function run-python adds the emacs data-directory to the PYTHONPATH in the emacs process-environment before running python; unfortunately, since this is the MS Windows emacs, its data-directory starts with a drive letter and a colon. When the Cygwin python initializes sys.path it splits PYTHONPATH at the colons, which means sys.path ends up with the drive letter as one component (usually interpreted as a relative path) and everything after the colon as another component. It that's a valid Cygwin pathname for the Emacs data directory (which is what the above mount command did), things work (accidentally).