Generalized Langevin equations (GLEs) are used to calculate angular velocity correlation functions (AVCFs) and orientational correlation functions (OCFs) of asymmetric top molecules in the high friction limit. Two exponential memory functions are shown to fit simulated AVCFs satisfactorily. These memory functions consist of an intense but quickly relaxed contribution (in-cage rotation) and a small but slowly decaying contribution (due to collective modes). An exact analytical expression for an arbitrary rank asymmetric top OCF is obtained up to terms of order O(t(6)). This result allows establishment of the correspondence between the short-time value of the memory function and the averaged magnitude of the external torque. Explicit formulas are derived for symmetric top OCFs when arbitrary (from slip to stick) boundary conditions are presumed. These formulas are proved to reduce to the conventional first cumulant expressions provided that molecular rotation around the symmetry axis is driven by a Gaussian stochastic process, The experimentally observed non-Gaussian behavior is suggested to be attributed to the preferential angular velocity reorientation due to a collision, and a convenient analytical model is proposed to describe this effect.