Power Steering Pully Stops
 

I have a 2002 Accent 1.6L and when I turn the wheels all the way too the right or all the way to the left the pulley stops spinning. Could this be that the pump is going bad or something else?

Stop doing that. The pump isn't going bad but if you continue to do that it will.

Turning the wheels all the way to the stops and then continuing to turn the wheel puts stress on the pump because it's trying to turn the wheels when it physically can't. The pump isn't bad, the driver is.