James,
Welcome to the wacky world of Pennsylvania backpacking! As another poster said, you can't camp on State Game Lands except along the AT. I've done out-and-back along the AT without any issues and doubt you'd really run into any problems if you're on the AT.
There are lots of other trails going through State Forest land where you can camp anywhere. The State Forest rules are different – and actually seem to be written specifically with backpackers in mind. You are not required to have a permit to spend the night on State Forest land unless you're spending more than one night in the same spot. This usually doesn't apply to backpacking.
There are two exceptions to this rule:
1 – When you're in a State Park – you cannot camp within the boundary of a PA State Park unless you're in a designated campground and have paid the appropriate fees.
2 – The Laurel Highlands Trail is probably not an exception this rule but it seems like it is…The 70-mile LHT is contained entirely within Laurel Ridge State Park and, as such, you are required to pay for and reserve specific sites if you're going to hike it. That's one of the reasons I haven't done the LHT – I like the flexibility to stop at 2:00 if I want or to go on until 8:00. With the reservation system of the LHT you have to get to your destination or risk a fine.
With that said, there are a lot of opportunities for backpacking in PA in addition to the couple already mentioned:
– Allegheny Front Trail (42 mile loop northwest of State College)
– West Rim Trail (30 mile linear trail along the western rim of the PA Grand Canyon)
– Old Loggers Path (27 mile loop north of Williamsport)
– Mid State Trail (300+ mile linear trail running South–>North through the center of the state)
Feel free to PM me if you have other questions…I'm always happy to help other backpackers.