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(Abridged) We develop a model for the cosmological role of mergers in theevolution of starbursts, quasars, and spheroidal galaxies. Combining halo massfunctions (MFs) with empirical halo occupation models, we calculate where majorgalaxy-galaxy mergers occur and what kinds of galaxies merge, at all redshifts.We compare with observed merger MFs, clustering, fractions, and small-scaleenvironments, and show that this yields robust estimates in good agreement withobservations. Making the simple ansatz that major, gas-rich mergers causequasar activity, we demonstrate that this naturally reproduces the observedrise and fall of the quasar luminosity density from z=0-6, as well as quasarLFs, fractions, host galaxy colors, and clustering as a function of redshiftand luminosity. The observed excess of quasar clustering on small scales is anatural prediction of the model, as mergers preferentially occur in regionswith excess small-scale galaxy overdensities. We show that quasar environmentsat all observed redshifts correspond closely to the empirically determinedsmall group scale, where mergers of gas-rich galaxies are most efficient. Wecontrast with a secular model in which quasar activity is driven by bars/diskinstabilities, and show that while these modes probably dominate at Seyfertluminosities, the constraints from clustering (large and small-scale),pseudobulge populations, disk MFs, luminosity density evolution, and hostgalaxy colors argue that they must be a small contributor to the z>1 quasarluminosity density.