Can I force users to join a group when registering? I would like everyone to be a member of "our Community" by default.
I want everyone to be a member of a site-wide group so that we can have a site-wide wiki, events &amp; all the other usual group stuff.

Do I miss the point? Is this already the case, or do I not really want what I think that I want?
I am not sure, but if Organic Groups has rules integration; you might be able to create a Rule which automatically adds the user to the desired group.