After reading this answer I found out that the space shuttle normally spent its time upside-down. Why is that? I'd guess it has to do with shielding from the sun, but I can't back that up with anything.
The main reason is heat rejection. NASA was asked this very question, and the answer was identified. Basically, the waste heat from the shuttle is expelled via the cargo bay doors. You don't want to ever point a radiator at the Sun, so the easiest thing is to point it at the Earth. Sometimes, if the heat was too high, they would actually point the shuttle away from the Sun in eclipse, but this was rare.
If space debris was the main reason, then the shuttle would actually fly with the belly towards the direction of motion. Most impacts of space debris will be head on. The shuttle did fly backward, with the tail in the direction of orbital motion. This protected it against debris, as the tail was the less critical portion of the spacecraft for small holes that Debris would cause. See this link.
Yes, one reason is that it is flown upside down (with the top facing towards Earth) to use the heat shield tiles to shield the astronauts from the sun, but I think a bigger reason is to shield from space debris.
One reason is to protect against space debris. Here on Earth, most of the space junk (small rocks and ice, etc.) that falls towards the planet burns up in the atmosphere before it can get to us. The space shuttle is outside the atmosphere, though, so it is much more exposed to debris (which may be traveling at very high speeds). The space shuttle's belly is designed to take intense heat and pressure so that it doesn't fall apart when it re-enters the atmosphere, and is therefore much better suited for taking hits from flying space junk.
During launch, it is for aerodynamic reasons, and line-of-sight with the ground:
"The orbiter flies upside down during the ascent phase. This orientation, together with trajectory shaping, establishes a trim angle of attack that is favorable for aerodynamic loads during the region of high dynamic pressure, resulting in a net positive load factor, as well as providing the flight crew with use of the ground as a visual reference. By about 20 seconds after lift-off, the vehicle is at 180 degrees roll and 78 degrees pitch."
Basically, the once-off fuel tank is taking the brunt of the wear and tear during the climb up through the atmosphere, and sheltering the orbiter somewhat. Although I don't have a reference for it, I remember reading somewhere that the communication antenna work best on the 'top' side of the orbiter, so pointing it at the ground is desirable when on orbit.