Pros:
Gives some HP back to the engine. I've heard as much as 10HP from someone who dyno'ed their car with water pump belt off vs. water pump belt on.QUOTE]
This is a myth, same as the electric fan-saves-horsepower myth. You need electrical power to drive the pump, (or fan) which comes from the alternator. It's much less efficient to mechanically drive an alternator, to produce electricity, to convert back to mechanical motion via an electric motor than it is to drive the pump mechanically in the first place.
Every one of the claims I read talks about power they gained by removing the drive belt, but conveniently forgets to mention how much extra load it puts on the electric system.
If you were to continue running the pump and fan after the engine shuts down,
1) what would you gain?
2) think how hard your alternator would have to work to recharge the battery next time you start the engine.