The state-to-state rates of collisional energy transfer within and between the rotational level manifolds associated with the Omega=1/2 and Omega=3/2 spin-orbit states of NO(X(2) Pi, nu=2) have been measured using an infrared-ultraviolet double resonance (IRUVDR) technique. NO molecules were initially prepared in a specific rovibronic level, for example, nu=2, Omega=1/2, J=6.5, by tuning the output from an optical parametric oscillator (OPO) to a suitable line in the (2,0) overtone band. Laser-induced fluorescence (LIF) spectra of the A (2) Sigma(+)-X (2) Pi (2,2) band were then recorded at delay times corresponding to a small fraction of the average time between collisions in the gas sample. From such spectra, the relative concentrations of molecules in levels populated by single collisions from the initially prepared state could be estimated, as could the values of the rate coefficients for the state-to-state processes of collisional energy transfer. Measurements have been made with NO, He, and Ar as the collision partner, and at three temperatures : 295, 200, and 80 K. For all collision partners, the state-to-state rate coefficients decrease with increasing Delta J (i.e., change in the rotational quantum number and rotational angular momentum) and increasing Delta E(rot) (i.e., change in the rotational energy). In NO-NO collisions, there is little propensity for retention of the spin-orbit state of the excited molecule. On the other hand, with He or Ar as the collision partner, transfers within the same spin-orbit state are quite strongly preferred. For transfers between spin-orbit states induced by all collision partners, a propensity to retain the same rotational state was observed, despite the large change in internal energy due to the spin-orbit splitting of 121 cm(-1). The results are compared with previous experimental data on rotational energy transfer, for both NO and other molecules, acid with the results of theoretical studies. Our results are also discussed in the light of the continuing debate about whether retention of angular momentum or of internal energy is the dominant influence in determining the rates of state-to-state rotational energy transfer.