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.
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.