We present the full results of our 3-year long Submillimeter Array survey of protoplanetary disks in the Orion Nebula Cluster . We imaged 23 fields at 880 \mu m and 2 fields at 1330 \mu m , covering an area of \sim 6.5 arcmin ^ { 2 } and containing 67 disks . We detected 42 disks with fluxes between 6-135 mJy and at rms noise levels between 0.6 to 5.3 mJy beam ^ { -1 } . Thermal dust emission above any free-free component was measured in 40 of the 42 detections , and the inferred disk masses range from 0.003 - 0.07 M _ { \odot } . We find that disks located within 0.3 pc of \theta ^ { 1 } Ori C have a truncated mass distribution , while disks located beyond 0.3 pc have masses more comparable to those found in low-mass star forming regions . The disk mass distribution in Orion has a distance dependence , with a derived relationship max ( M _ { disk } ) = 0.046M _ { \odot } ( d/0.3pc ) ^ { 0.33 } for the maximum disk masses . We found evidence of grain growth in disk 197-427 , the only disk detected at both 880 \mu m and 1330 \mu m with the SMA . Despite the rapid erosion of the outer parts of the Orion disks by photoevaporation , the potential for planet formation remains high in this massive star forming region , with \approx 18 % of the surveyed disks having masses \geq 0.01 M _ { \odot } within 60 AU .