Please stop voting this guy up, while simultaneously voting down the numerous posts that are correct.
Four satellites are required because there are four unknowns, and only one measurement per satellite available, irrespective of precision or lack thereof.
Here's some quotes from Global Positioning System so we can all stop agreeing with the loudest person instead of the facts:
"About nine satellites are visible from any point on the ground at any one time, ensuring considerable redundancy over the minimum four satellites needed for a position."
"The receiver uses messages received from satellites to determine the satellite positions and time sent. The x, y, and z components of satellite position and the time sent are designated as [xi, yi, zi, ti] where the subscript i denotes the satellite and has the value 1, 2, ..., n, where n >= 4."
"Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship or aircraft may have known elevation.
The time precision required for a fix of any reasonable accuracy requires atomic clocks. You can't carry atomic clocks in your pocket, they're a tad too big for that. There is no way to know the time on the satellites from the ground, because you don't know where you are, and hence how far the satellites are from you, and hence the delay added to the signals. You can use three satellites to figure out where you are, if you know what time it is, but you don't. Adding a fourth satellite in the mix lets you solve for all four unknowns in the equation. Note the exception in the wiki article applies only in some rare cases, like the GPS units used by ships, not the GPS units handed out to most military personnel.
THIS HAS NOTHING AT ALL TO DO WITH SELECTIVE AVAILABILITY.
The military encryption simply reduces the precision of the solution, it doesn't actually change the number of unknowns and hence the equations in any way. A civilian marine GPS could locate itself with just 3 satellites even with selective availability enabled, as long as it assumes that it's at 0 elevation. In all other cases, four satellites are required, even for military units.