Chemically synthesized PbS, CdSe, and CoPt(3) nanocrystals (NCs) were self-assembled into highly periodic supercrystals. Using the combination of small-angle X-ray scattering, X-ray photoelectron spectroscopy, infrared spectroscopy, thermogravimetric analysis, and nanoindentation, we correlated the mechanical properties of the supercrystals with the NC size, capping ligands, and degree of ordering. We found that such structures have elastic moduli and hardnesses in the range of approximately 0.2-6 GPa and 10-450 MPa, respectively, which are analogous to strong polymers. The high degree of ordering characteristic to supercrystals was found to lead to more than 2-fold increase in hardnesses and elastic moduli due to tighter packing of the NCs, and smaller interparticle distance. The nature of surface ligands also significantly affects the mechanical properties of NCs solids. The experiments with series of 4.7, 7.1, and 13 nm PbS NCs revealed a direct relationship between the core size and hardness/modulus, analogous to the nanoparticle-filled polymer composites. This observation suggests that the matrices of organic ligands have properties similar to polymers. The effective moduli of the ligand matrices were calculated to be in the range of approximately 0.1-0.7 GPa.