Depends on the pan, the pick-up and mostly on the pump.
Stock stuff, you typically shoot for about 3/8" to 1/2". High volume, you are talking typically 1/2" to 3/4". Titan recomends a minimum of 3/4" and would like an ideal clearance of 1".
The reason is depending on the volume of the pump and pickup design, you might induce cavitation with the pickup to close to the bottom of the pan. Oil cant flow into the pick-up area fast enough. The down side of setting the pickup excessivly high is the quart or two of oil that is lower than the pick-up is not capable of flowing through the system.