Cygwin's default terminal sucks. I'm sure I don't need to explain why. You can use rxvt instead, see http://c2.com/cgi/wiki?BetterCygwinTerminal
However, there's a much better option. PuTTYcyg is a patched version of PuTTY that lets you connect to your local cygwin installation.
Download it here: http://code.google.com/p/puttycyg/