I've got the same exact problem on a Mac Mini and an iMac, neither of which have any special port-blocking stuff installed (e.g. PeerGuardian) and the Firewall is off as well. Other similar applications work fine; e.g. Skype, ooVoo and I've never had any other internet connection issues with any other applications.
The error message from FaceTime is "Could not sign in. Please check your network connection and try again."
The DNS solution did not work for me. I don't have any means to connect through an alternative ISP or I'd try that next.
Apple support says to check that the required ports are open. I have no ports blocked on my personal router and have sent a message out to my ISP to check if they are blocking any ports - waiting to hear back on that.
Sure seems like there are plenty of Apple customers seeing this problem. I know it's just a 99-cent app, but it is from "Apple" from which I have higher expectations than the freeware/adware options.
sigh... hopefully my ISP has some good news for me.