What was the fastest flight by man without an aircraft?

Felix Baumgartner holds the world record for the fastest flight speed without an aircraft when he achieved a speed of 843.6 miles per hour after jumping 128,100 feet. The jump took a little over 9 minutes.

On October 14, 2012, Baumgartner jumped from a custom-made space capsule carried 24 miles in the sky by a helium balloon. Thirty four seconds into his free fall, he went supersonic, meaning he broke the sound barrier, and was in free fall for more than 4 minutes.

In October 2014, Alan Eustace broke Baumgartner's record for the highest jump, jumping 135,892 feet. He did not break the speed record though. Despite going supersonic, Eustace only reached a top speed of 807.78 miles per hour.