Panels with substantially integrated watershedding features may be installed on the roof a house or other structure in lieu of traditional roofing materials. The panels include a body formed from a mixture of filler materials and polymeric binder materials, which can include recycled materials, with watershedding features generally formed with and/or integrated with the panels. The panels also can be installed in overlapping courses along a roof with the watershedding features incorporated along one or more peripheral edges. The watershedding features of adjacent panels further can cooperated to collect and divert water away from the upper surfaces and/or away headlap and/or sidelap joints defined between the panels.