There are landing fees, or if you want to call them, tie down fees. Most of the time if you buy gas, the FBO will wave the fee but if you don't they can charge you. I have a buddy that has a 150 and hes been charges almost 30 bucks at one airport.
But as for true landing fees, GA pilots don't have to pay them, that only comes into play if you land at a class B airport and are above a certain weight based off the make of your aircraft. So unless your John Travolta, i wouldn't worry about it to much.