The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anticorrelation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a Gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.