No fees or paid permits are required to access the Appalachian Trail (A.T.) for simply walking. However, some New England campsites impose fees and you must obtain permits for backcountry camping in two national parks on the A.T. Entrance or parking fees are collected at some national and state parks that the Trail passes through, but the vast majority of access points are free and require no advance permit or reservation.
More information about regulations pertaining to camping and fires along the A.T. can be found here.
A permit is not required to begin a thru-hike of the entire A.T.,
but you are strongly recommended to participate in the voluntary thru-hiker registration.