Does it hurt to leave your cell phone on the charger?

For most devices, yes. There is an issue called overcharge where power is being stored with nowhere to go. Keeping your phone plugged in too long can damage the internal parts of the battery, and eventually leads to less battery life and internal memory problems. One way to prevent this is to cycle the battery several times: unplug it, run it down to where it's dead or almost there, charge all the way (but not overcharge), run it down again, and charge one more time. However, each battery has a certain amount of cycles before the battery runs out quickly no matter how good you are to it.

Prescrition: cycle your phone several times as described. If battery life does not improve, invest in new battery unless shortened battery life is still satisfactory...