Orbiting a planet is like learning to fly in Hitchhiker's Guide to the Galaxy. You fall, but miss the ground. During the orbit, you are being accelerated towards the center of mass of the object you are orbiting. If you were a stationary object, SPLAT!! However, if you have enough forward velocity, you will miss the planet and go around one more time.
So long as you are well outside the atmosphere, this will continue almost indefinitely. The atmosphere will impose drag, which will slow you down, so you won't miss on that next pass, SPLAT!!
If your orbit happens to be circular, and you are at the right speed and altitude, you will be moving in concert with the rotation of the planet, like all those nifty Dish Network/Direct TV/GPS satelites.
One thing that has often bothered me is shows where ship lose power and start falling from orbit. What sort of orbit were they in? Were they deliberately operating slower than their altitude required and using thrust to counter gravity? Were they actually orbiting so low as to brush the atmosphere and require thrust to keep up speed? The shuttle (when it's flying) stays up for days without any power. The ISS goes months at a time with just the periodic boost. Somebody needs to teach these navigators how to calculate an orbit.
