In this paper we examine the asymptotic long time dynamics of quasi two-dimensional colloidal suspensions over a wide range of concentrations. At low concentrations the dynamics is determined by uncorrelated binary collisions among the constituent particles. These collisions among the particles lead to logarithmic corrections to the well-known linear growth in time of the mean squared displacement of the particles in the suspension. The self-scattering function of the suspension can be related to the mean squared displacement via the Gaussian approximation, which we examine in detail for systems of low concentration. At higher concentrations caging effects influence the dynamics of the suspension, which we account for by developing a formal mode coupling theory for colloidal systems from first principles. Equations for the dynamics of the memory functions that account for caging effects are derived and solved self-consistently, for the case of instanteous hydrodynamic interactions, by utilizing the Gaussian approximation for the scattering functions of the colloidal system and assuming a particular form for the cumulants of the position. We find that the functional form suggested by Cichocki and Felderhof for the time dependence of the mean squared displacement of quasi two-dimensional colloidal systems in the limit that hydrodynamic interactions are instantaneous is compatible with the predictions of mode coupling theory. Furthermore, we explicitly evaluate the long time diffusion coefficient and other parameters as a function of concentration.