For what it's worth, the oldest continually running game still currently being played on PBW is an affair called "Us against the Computer". It was started in June of 2001.

It's currently up to turn 180 and appears to be getting about a turn every other week recently. Not sure if it's had faster and slower periods during it's history. That is likely. That's usually how it happens.
On the other hand a game I am in that started on August 4th is already up to turn 94.
But that is slow compared to some of the games I have been in and seen. I had one game where we were averaging 7 or 8 turns a day for a couple weeks. And I have heard of games getting in 25 to 30 turns a day. It all depends on how dedicated the players are.
It also helps to have just a few players. Typically the fewer players the faster the turns.
Geoschmo