What is the maximum altitude a skydiving plane can fly?
Qualifier: I am a master parachute rigger and taught sport skydiving for 10 years.

Standard jump altitude is 12,000 feet AGL - this is one turn of the standard parachutist's altimeter. This height provides 1 minute of freefall, is within reach of a Cessna with a decent engine and does not require supplementary oxygen. For most places, this means an operating altitude between 12,000 and 15,000 feet MSL. 

Dropzones in high areas like Denver will reduce their jump altitude to 9,500 feet AGL mainly because the piston-powered planes take too long to climb higher and/or the upper part of the climb runs into the oxygen zone.