Hubble orbits approximately 540 kilometers above Earth.
That altitude places the telescope in low Earth orbit, well above the atmosphere but close enough for space-shuttle servicing missions during the shuttle era. Hubble does not remain at exactly 540 kilometers: atmospheric drag, orbital boosts, and mission operations cause its altitude to vary over time. The figure is therefore a useful rounded description rather than a permanent measurement.
Hubble travels around Earth roughly once every 95 minutes. Its orbit is inclined about 28.5 degrees to the equator, allowing it to observe much of the sky while avoiding some regions near the poles.
A common mix-up is confusing Hubble's orbital altitude with its distance from Earth when an image is taken or with the altitude of the International Space Station, which is also in low Earth orbit but generally flies lower. Hubble's position above most of the atmosphere is crucial because atmospheric turbulence would otherwise blur its observations.