My mom is in a very low-key book club-- they read one book a year. (!)
My husband and I and a couple of other close friends tend to try to get one another to read books we've just read and liked so we'll have someone to talk with about them. The frustrating thing there is that generally we've got one copy between us, so we have to pass it around and wait for others to finish it.
So I suppose if we were all on one Connect account or something, we could all be reading new books at the same time, except that the books we're sharing generally aren't available on Connect (SF&F) and one person hates gadgets and another can't see the point of spending money on an electronic reader when we can just buy the book and share that.

I think the days of ebook reader clubs aren't here yet, at least for my group.