This paper describes theoretical and computational research aimed at understanding the vibrational state distributions of triatomic molecule products which are produced in diatom plus diatom reactive collisions. The primary computational tool in this research is quasiclassical trajectories, wherein the vibrational states of the products are determined by numerically calculating the "good" actions associated with vibrational motion. Four exothermic reactions are considered : OH + H-2(D-2), H-2(+) + H-2, OH + CO, and NH + NO. The first two of these reactions are direct reactions which produce nonlinear product triatomics while the second two involve the formation of short-lived complexes and linear product triatomics. Our analysis considers energy partitioning between vibration, translation, and rotation and state distributions associated with the vibrational modes. Common features among all the reactions are that bend modes excitation is significant and that stretch mode excitation is accompanied by significant bend excitation. None of the vibrational distributions are statistical, but only the HOD stretch modes in OH + D-2 and the bend mode of CO2 and N2O in OH + CO and NH + NO show easily understood mode-specific propensities.