We study the Brownian motion of quasi-two-dimensional suspensions of micron-sized particles parallel to a single wall. The dynamics of a suspension near a single wall have two characteristics; the self diffusivity is smaller than in unconfined suspensions, and the hydrodynamic interactions decay with inter-particle distance r as 1/r³. We follow the change in the self diffusivity and hydrodynamic interactions as a function of particle area fraction, ϕ. As expected, the self diffusion decreases as ϕ increases for low ϕ's. However, self diffusivity surprisingly increases above ϕ=0.42. We also observe strongly correlated motion between particles separated by a distance much larger than their distance from the wall. This long-range hydrodynamic coupling is enhanced as particle density increases. Interestingly, we see a deviation from this trend at intermediate ϕ (0.40-0.52), where we observe a local minimum in the long-range hydrodynamic interactions. We also compare the experimental results to a theory based on three body effects.