This page lists and compares Go applications that are available to Facebook users.
Most games seem to be playable on-line as well as in turn-based mode.
Please discuss bugs, feature requests etc. on the associated Facebook forum pages.
Facebook changed the API needed for getting user authentication so it's impossible for Go - Online Game to recognize you. Unfortunately simple fix attempts didn't work and I have no time to investigate further at the moment. It might well be that with the API change Facebook destroyed this application. I'm sorry. If I'm not able to get it up and running by New Year, I will delete this application."
axd: I got fed up trying those apps. Actually I resigned right away, even twice in a row, after the very first move. Didn't bother testing them all, by lack of interested people. I have the impression that these applications are a waste of time, some are no more than gadgets, or even worse, means to get the attention to a website outside FB. So for the moment, they all get a big thumbs down, yes, even without having seen them in action... Maybe when they ripe more I'll give them another look.