Although it certainly seems logical that it could, for certain reasons the shuttle actually has a limited range of orbits--called "inclinations"--that it can achieve. An orbit inclination is the angle of the spacecraft's path as it crosses the equator. Kennedy Space Center sits at 28.5 degrees latitude north of the equator. Since it would take much more fuel for the shuttle to head south, 28.5 degrees is the minimum inclination the shuttle can fly. If you were to look at the path the shuttle flies across the Earth on a Mission Control Map, the shuttle would fly from 28.5 degrees north of the equator to 28.5 degrees south of the equator. These types of orbits are called "low inclination" orbits and do not cover much of the Earth's land masses.

Also, since NASA does not want the shuttle to be launched over land, the shuttle cannot be launched directly over North America, so the farthest north the shuttle can fly is 62 degrees north of the equator to 62 degrees south of the equator. These types of orbits are called "high-inclination" orbits, and are often used to launch commercial or military satellites, and for Earth Observation photography. Because they can see much more of the land masses of the Earth, many astronauts prefer these types of orbits.