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Molecular dynamics (MD) simulations are used to compute the equilibrium dynamics of a single component fluid with Yukawa interaction potential v(r) = (Ze)^2 exp(−r/λs )/4π eps_0 r. This system, which is known as the Yukawa one-component plasma (YOCP), represents a simplified description of a non-ideal plasma consisting of ions, charge Ze, and electrons. For finite screening lengths λs, the MD results are used to investigate the domain of validity of the hydrodynamic description, i.e., the description given by the Navier-Stokes equations. The way in which this domain depends on the thermodynamic conditions of the YOCP, as well as the strength and range of the interactions, is determined. Remarkably, it is found that the domain of validity is completely determined by the range of the interactions (i.e., λs); this alone determines the maximum wave number k_max at which the hydrodynamic description is applicable. The dynamics of the YOCP at wavevectors beyond k_max are then investigated; these are shown to be in striking agreement with a simple and well known generalisation of the Navier-Stokes equations. In the extreme case of the Coulomb interaction potential (λs = ∞), the very existence of a hydrodynamic description is a known but unsolved problem [Baus & Hansen, 1980]. For this important special case, known as the one-component plasma (OCP), it is shown that the ordinary hydrodynamic description is never valid. Since the OCP is the prototypical system representing a non-ideal plasma, a number of different approaches for modelling its dynamics have been formulated previously. By computing the relevant quantities with MD, the applicability of a number of models proposed in the literature is examined for the first time.