Physics opportunities with future proton accelerators at CERN

We analyze the physics opportunities that would be made possible by upgrades of CERN's proton accelerator complex. These include the new physics possible with luminosity or energy upgrades of the LHC, options for a possible future neutrino complex at CERN, and opportunities in other physics including rare kaon decays, other fixed-target experiments, nuclear physics and antiproton physics, among other possibilities. We stress the importance of inputs from initial LHC running and planned neutrino experiments, and summarize the principal detector R&D issues.