The Mars Exploration Rovers Spirit and Opportunity investigated the physical properties of Martian regolith in 7 wheel trenches and 20 wheel scuffs distributed along traverses at Gusev crater and Meridiani Planum. Specialized wheel-trenching sequences allowed analysis of wheel motor and suspension telemetry to determine regolith friction angle phi and cohesion c at trench sites. Friction angles were 30 degrees - 37 degrees, and cohesions were 0-2 kPa. Simpler wheel-scuff maneuvers were analyzed for cohesion by assuming the range of phi determined from trenches; cohesions in wheel-scuffed regoliths were from 0 to 11 kPa. Regolith phi and c can be related to regolith origins. Grain sorting, compaction, shape, size, and angularity influence phi. Impact cratering and aeolian processes have affected grain angularity and sorting of Martian regolith at both Mars Exploration Rover (MER) landing sites and contend in opposing ways to determine grain characteristics in the regolith. Friction angles are consistent with dry, rigid, nonplaty grains with particle size frequencies dominated by very fine sand (as seen by the Microscopic Imager or MI) with at least some grain rounding (unresolved by MI), reflecting physical weathering from aeolian saltation. Friction angle results from MER trenches therefore indicate that regolith states are between fully mature aeolian materials and impact debris. MI and color Pancam views show trench tailings and trench floors are redder, brighter, and have more intermixed extremely fine (unresolved) grains than regolith closer to the surface disturbed and exposed only by rolling tracks.