Curious to know this. It's typical orbit is around 200-250 miles above the earth's surface, although it will be going higher when it services Hubble. But does anyone know what is the limit for how high the Space Shuttle can orbit the earth? Thanks!

There really isn't just one answer to this for a number of reasons. First, there is no vehicle called The Space Shuttle. There are a number of space shuttles built at different times with somewhat different capabilities. For a given space shuttle the maximum orbit that it could attain would be carrying no payload. This would make the mission meaningless. That being said, the maximum orbit for a "practical" mission would be around 400 miles. That would be carrying a payload somewhat less than a "normal" ISS mission.

If you can read the words on my avatar you can tell that I used to work or NASA, mostly during the lunar landing missions. The Space shuttle is designed to operate in space, that is, away from the atmosphere of Earth and could, at least theoretcially be used for extended missions away from Earth, such as going to the Moon. Of couse this would require major modifications, but the point is that once a vehicle is equipped to operate outside the Earth's protective envelope, the question of how high it can go really doesn't apply. It would be more accurate to ask how far away from Earth it can go. The question of how high something can go is better applied to things like airplanes and ballons.

A space shuttle could theoretically go an infinite distance from the surface of the planet. Its not so much the distance, it's the amount of time it's out on a mission. It's a matter of how much fuel and resources it can carry to return the crew back to earth safely.
The furthest it has ever gone is the Hubble orbit.