I am not quite sure what happened ... alt-backspace won't backward-kill-word any more in my Cygwin install. It looks like I did an update on 7/17/2013, not sure what was in the update, I usually just pull whatever's the latest version of the modules I have.
Backspace itself works, it's with the alt that nothing happens. I tried both right and left alt keys.
I couldn't figure out where to start here - I didn't change anything in my Mintty settings, or in my .inputrc at all. I'm at a total loss...
Thanks!