Retinal ganglion cells exhibit substantial correlated firing: a tendency to fire nearly synchronously at rates different from those expected by chance. These correlations suggest that network interactions significantly shape the visual signal transmitted from the eye to the brain. This study describes the degree and structure of correlated firing among the major ganglion cell types in primate retina. Correlated firing among ON and OFF parasol, ON and OFF midget, and small bistratified cells, which together constitute roughly 75% of the input to higher visual areas, was studied using large-scale multi-electrode recordings. Correlated firing in the presence of constant, spatially uniform illumination exhibited characteristic strength, time course and polarity within and across cell types. Pairs of nearby cells with the same light response polarity were positively correlated; cells with the opposite polarity were negatively correlated. The strength of correlated firing declined systematically with distance for each cell type, in proportion to the degree of receptive field overlap. The pattern of correlated firing across cell types was similar at photopic and scotopic light levels, although additional slow correlations were present at scotopic light levels. Similar results were also observed in two other retinal ganglion cell types. Most of these observations are consistent with the hypothesis that shared noise from photoreceptors is the dominant cause of correlated firing. Surprisingly, small bistratified cells, which receive ON input from S cones, fired synchronously with ON parasol and midget cells, which receive ON input primarily from L and M cones. Collectively, these results provide an overview of correlated firing across cell types in the primate retina, and constraints on the underlying mechanisms.