I've tried msysGit and Git on Cygwin. Both work just fine in and of themselves and both run gitk and git-gui perfectly.
Now how the heck do I configure a mergetool? (Vimdiff works on Cygwin, but preferably I would like something a little more user-friendly for some of our Windows-loving coworkers.)
Under Cygwin, the only thing that worked for me is the following:
git config --global merge.tool myp4merge
git config --global mergetool.myp4merge.cmd 'p4merge.exe "$(cygpath -wla $BASE)" "$(cygpath -wla $LOCAL)" "$(cygpath -wla $REMOTE)" "$(cygpath -wla $MERGED)"'
git config --global diff.tool myp4diff
git config --global difftool.myp4diff.cmd 'p4merge.exe "$(cygpath -wla $LOCAL)" "$(cygpath -wla $REMOTE)"'
Also, I like to turn off the prompt message for difftool:
git config --global difftool.prompt false