What causes these sleeping processes that I see in top? If I were to call PHP's sleep() function, would that add to the sleeping count I see in top? Are there any disadvantages to having a high number in sleeping?
A process is sleeping when it is blocked, waiting for something. For example, it might have called read() and is waiting on data to arrive from a network stream.
sleep() is indeed one way to have your process sleep for a while. Sleeping is, however, the normal state of all but heavily compute-bound processes - sleeping is essentially what a process does when it isn't doing anything else. It's the normal state of affairs for most of your processes to be sleeping - if that's not the case, it tends to indicate that you need more CPU horsepower.