We report results of first-principles calculations based on the projector augmented wave (PAW) method to explore the structural, thermodynamic, and electronic properties of cubic (3C) and hexagonal (6H, 4H, and 2H) polytypes of II-VI compounds: ZnS, ZnSe, and ZnTe. We find that the different bond stacking in II-VI polytypes remarkably influences the resulting physical properties. Furthermore, the degree of hexagonality is found to be useful to understand both the ground-state properties and the electronic structure of these compounds. The resulting lattice parameters, energetic stability, and characteristic band energies are in good agreement with available experimental data. Trends with hexagonality of the polytype are investigated.