How fast can a human travel in space?

Answer 1

At 99.999999999999999999999999% of the speed of light, just like everything else that has mass.

But also take in account acceleration, safely the fastest speed to accelerate is a constant 2g acceleration without killing your astronaunts.

Answer 2

The fastest speed at which humans have traveled in space is about 24,790 miles per hour (39,897 kilometers per hour), achieved by the Apollo 10 mission. This speed was necessary to escape Earth's gravity and travel to the Moon.