We suggest the M|G|input process as a viable model for network traffic due to its versatility and tractability. To gauge its performance, we study the large buffer asymptotics of a multiplexer driven by an M|G|input process. We identify the process as short or long-range dependent by means of simple tests. The decay rate of the tail probabilities for the buffer content (in steady-state) at the multiplexer is investigated using large deviation techniques suggested by Duffield and O'Connell. The appropriate large deviations scaling is found to be related to the forward recurrence time for the service time distribution, and a closed-form expression is derived for the corresponding generalized limiting log-moment generating function associated with the input process. Two very different regimes are identified. We apply our results to cases where the service time distribution in the M|G|input model is (i) Rayleigh (ii) Gamma (iii) Geometric (iv) Weibull (v) Log-Normal and (vi) Pareto - cases (v) and (vi) have recently been found adequate for modeling packet traffic streams in certain networking applications. Finally, we comment on the insufficiency of the short or long- range dependence in the process in clearly describing buffer dynamics.