Support structures for footwear and the like include contact surface-contacting members (e.g., outsole structures) having an exterior surface that includes: (a) a recessed segment extending longitudinally from a forefoot to a heel portion, (b) plural lateral motion inhibiting traction elements in the lateral, forefoot portion, and (c) plural medial motion inhibiting traction elements in the lateral, heel portion. The recessed segment provides a flex line about which the medial and lateral sides of the surface-contacting member can move to independently engage and disengage from a contact surface as a wearer's weight shifts. In at least some structures, the lateral side of the foot-supporting member may be less flexible and/or more stable than the medial side. Support structures of the types described above can allow more of the surface-contacting member to remain in contact with the ground and provide a solid base or support for the movement or activity.