As of 2014, the fastest rocket ship, NASA's New Horizons spacecraft, was recorded at a speed of 36,000 miles per hour. The speed a spacecraft travels depends on if it is ascending, orbiting or returning to Earth.
In order for a spacecraft to escape the gravitational pull of Earth, it must travel at a speed of at least 7 miles per second. This is referred to as the escape velocity and usually takes about 8.5 minutes. Once the spacecraft gets to space, it must maintain a speed of 17,200 miles per hour to remain in orbit. To leave the orbit and return to Earth, the spacecraft drops its speed to below 750 miles per hour. After this, the commander flies and lands the spacecraft.