Yes it does,
Offhand I dont know what it is, but look at the data sheet under maximum operating conditions. It will be about the same as the maximum operating voltage.
Look at the data sheet output voltage swing spec. For the National LM741 the swing look like 4 volts less than Vsupply for 10k load and 5v less than supply for 2k load.
Always consult data sheet as all op amps are not created equal.
Like mentioned before. It depends of the specific opamp you're using. They are different. Read a datasheet that contains a simple schematics of the output stage, and you'll probably see what limitations it have.