We report computer simulations of single-chain polymer adsorption dynamics. The time required for adsorption is obtained as a function of the chain length and chemical composition of homopolymers, diblock copolymers, and random copolymers. The copolymers are composed of type A segments that adsorb strongly (10 k(B)T per segment) and type B segments that have no attractive interactions with the surface; homopolymers are composed exclusively of type A segments. A relaxation function for adsorption is defined as a normalized number of adsorbed segments; it is calculated by averaging over hundreds of statistically independent adsorption trials. Relaxation is nonexponential at short times, while at intermediate times the relaxation is described by a single time constant. At the longest times, a few long-lived nonequilibrium states are observed, and the relaxation is again nonexponential. A relaxation time for adsorption is defined as the time constant for the relaxation in the intermediate region. This relaxation time varies with the chain length of homopolymers according to a power law, with an exponent equal to 1.50 +/-0.04 when excluded volume interactions are ignored and 1.58 +/- 0.04 when excluded volume interactions are enforced. For diblock copolymers, the adsorption time of single chains is almost independent of the nonadsorbing (type B) block length. For random copolymers with a fixed number of adsorbing segments, the chain length scaling of the adsorption time is similar to the scaling of the relaxation time of the end-to-end vector autocorrelation function in free and tethered chains.