The world record for the highest skydive is held by Joe Kittinger, an Air Force Captain who in 1960 jumped out of a balloon from an altitude of 102,800 feet; about 20 miles up, or three times as high as most jet airplanes fly.
At that height, sky diving is perhaps better termed "space diving" because 1. the sky is black as night 2. you can easily see what looks like the edge of the atmosphere on the horizon and 3. the pressure is so low and conditions so cold that you would die a quick, freezing, blood boiling death if you were ever to remove your pressure suit.
Never content to let records stand, several people have made serious attempts to break that record, and at least one has died trying. In 2010 there are two planned assaults on Kittinger's mark: France's Michel Fournier and Austrian daredevil skydiver Felix Baumgartner each have projects on the table that aim to break the mark by jumping from heights of 130,000 and 120,000 feet, respectively.
When Kittinger stepped out of his balloon fifty years ago, he described feeling no sensation of falling — he had to roll onto his back and see his craft rushing away from him into the black sky to understand what was happening. In fact he was moving faster than the speed of sound, and he remains the only person ever to do that without a vehicle, as he describes in this astounding retelling of the event:
Now, Fournier has been trying for years to accomplish his feat — problems with government permissions, weather, and health have kept his attempts grounded. He's planning to give it another go this May, but now he's got serious competition from Baumgartner. Although he's attempting to jump from a lesser height, the Austrian has cobbled together sponsorship from Red Bull, and even manages to get the great Kittinger himself on the project team.
It should be said that there's real value in jumps like these. If successful, they will prove that the human body can withstand the incredible stresses of a free fall that exceeds mach 1. They might even pave the way for an emergency abort system for astronauts launching from Earth.
(Incidentally, this wouldn't work for skydiving off the International Space Station, which orbits at around 205-210 miles above Earth's surface. Plus the speed required to be in orbit means a human in a pressure suit would be barbecued by the heat of re-entry into the atmosphere.)