The only one I know of is "Perfect Strangers Online - P.S. I Love You!" here (https://www.facebook.com/groups/148827065152897/).

That Facebook page is actually for one of the best Perfect Strangers fan sites I have seen for the show, by the way. The fan site does a wonderful job and I know they've been mentioned on this site here in the past. (I love Perfect Strangers, by the way. Such a great show! I'd love to see Seasons 3-8 come to DVD soon.):) :cool:
I'm sure plenty of other shows have Facebook pages as well- I think the question is: how many are just fan pages put together and how many are official pages from the studios? I'm pretty sure the Star Trek group is an official one from Paramount though.