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In this study, we implement first-principles calculation to study the physical and chemical properties of two-dimensional (2D) hexagonal crystals. The ab initio results of the crystallographic, elastic, and electronic band-gap parameters of C, Si, Ge, BN, CN, SiN, and SiC monolayers are presented. Similarly to graphene, CN and BN are among compounds with the highest 2D elasticity. The in-plane elastic moduli of Si and Ge monolayers are relative small. C, Si, and Ge monolayers are semimetal. All the four binary 2D crystals are semiconductors with wide band gaps. Two typical 2D hexagonal lattice structures, i.e., sp(2) flat and sp(3) rumpled configurations, are classified. The orbital sp(2)-hybridization in graphene and 2D BN is verified by angular-momentum projected atomic density of state calculation. 2D SiC is basically in sp(2)-hybridization. The orbital hybridization of Si, Ge, CN, and SiN monolayers is of the sp(3)-type on the whole. In view of the structural and chemical features of these monolayers, different methods for the experimental preparation of 2D crystals are suggested.