There's not a whole lot, I'm afraid. One of the more popular ones is Dia, although for the limited functions it does support, Kivio is slicker. Dia has an odd sense of scale and doesn't support rotated objects. And none of them support adding user-defined properties to graphical objects.
I actually started an open-source project to meet or (better yet) exceed the abilities of Visio (http://mtsdraw.mousetech.com), but I'm afraid that volunteer assistance in it has been fairly small, and I only get to work on it when I haven't got something revenue-producing to do instead.
Customer surveys are for companies who didn't pay proper attention to begin with.