This is something of a mystery. I just installed Cygwin on my Windows machine (Windows 8). The very first thing I tried was git clone (I was cloning a private repository using ssh, rather than anything on github). It announced cloning into blah-blah-blah, and then just froze. I waited several minutes, and nothing. I looked at the directory, and there was a directory created with the .git subdirectory, but nothing else. It never got around to asking for my password.
I am able to use git from a Windows command prompt, and the git shell that I downloaded from the Git website works. So there's no problem with my git connection. It's just git under Cygwin.
You might ask why I'm bothering, if I can use git outside of Cygwin. It's just because I'm trying to debug some git hook scripts that I wrote, and I want them to be usable by someone using git under Cygwin. But I can't even get to the point where the git hooks are called.