Funny timing for this - a few hours ago, I decided I needed more of a minimal word processor (although I'm not going as far to delete Word.) I stumbled across WriteMonkey (http://writemonkey.com/) and so far, I love it.
I found parts of WM like the giant context menu with icons for every entry, ability to enable typewriter noises and other little features detracted from the overall experience but it's still a solid app.
Since switching to OS X I've used Byword but recently tried out iA Writer and am considering a purchase.
Note: this only runs on Windows