The binary collision of water drops in the air is studied by two-dimensional numerical simulation utilizing smoothed particle hydrodynamics with adaptive spatial resolution. The numerical method is validated by comparing the simulation with experiment. Three basic modes of equal-size drop collision are observed in numerical simulations at Weber number 3≤We≤120 and impact parameter 0≤x≤0.8, namely, reflexive separation, stretching separation, and coalescence collision. Based on the numerical results of different collision modes, the specific phenomena, evolution patterns, and physical principles are discussed. In particular, the detailed processes of the necking phenomenon and the propagation of surface wave in separation collision are obtained, corroborating the "end-pinching" theory proposed in the literature. At higher Weber numbers, the recoalescence of satellite drops is observed. The collision of unequal-size drops is also investigated. The effects of three dimensionless parameters, namely, drop diameter ratio, Weber number, and impact parameter are discussed. The physical mechanisms of some special phenomena are expressed in detail.