The record was held for a very long time by Colonel Joe Kittinger who managed a staggering freefall time of 4 minutes 36 seconds jumping from an altitude of 102,800ft (also an altitude record).
Since then, wingsuit skydiving has taken over the record setting. The discipline still involves freefall so is applicable, however it changes frequently. Adrian Nicholas set the first of these wingsuit records in March 1999 with a freefall time of 4 minutes 55 seconds. Currently, a trio of Spanish skydivers (Santi, Toni and Alvaro) hold the record at 6 minutes 47 seconds, but this will undoubtedly increase as time goes on.
Making a wingsuit record like this requires quite a few things:
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There is really no limit to how high you can jump from, but it gets complicated because of the need for oxygen equipment and possibly pressure suits.
Many normal jump operations are from 13500' (4200m) all the time, which does not require oxygen. Above 15000' and up to 24000' (7300m) you can jump but you need to have oxygen onboard the aircraft for the jumpers and the pilot.
Above 24000' you have to have a freefall oxygen system which now becomes extremely expensive and complex, not to mention cold. There have been several sport parachute jumps made from just above 30,000' (9500m) but these are rare, and expensive. It is extremely cold at these temperatures and equipment malfunctions can be fatal. With no oxygen at 30,000' you could be unconscious in 30-40 seconds.
The world record jump is 106000' (32000m) by Joe Kittenger back in the 1960's as he jumped from a balloon on the edges of outer space as a military test jump. He was wearing a space suit and associated special equipment. There are new attempts underway recently to ry and break this record, but it has not been done yet.
Grant Denyer and A.J. Hackett bungee jumed from a helicopter 984 ft. above the water near Bondi Beach.
Apparently it is now 128,000', Felix Baumgartner set the new record yesterday over New Mexico. Most skydives are done from 13500' or less.