Note: for some reason, this seems slow, so I don't recommend changing your prompt as the file says

You can give bash git <tab> completion for things like commands, branches, switches etc...  To do this, you need to download a bash completion file or load the appropriate git-completion package, such as with cygwin.  Then you need to source this file in bash, probably in your .profile file.

===== External Links =====
  * http://www.viget.com/extend/a-gaggle-of-git-tips/
  * http://www.wincent.com/a/about/wincent/weblog/archives/2007/12/bash_completion.php
  * http://marioaquino.blogspot.com/2009/02/git-tab-completion-from-cygwin.html