We study the double-diffractive production of various heavy systems (e.g. Higgs, dijet, tt and SUSY particles) at LHC and Tevatron collider energies. In each case we compute the probability that the rapidity gaps, which occur on either side of the produced system, survive the effects of soft rescattering and QCD bremsstrahlung effects. We calculate both the luminosity for different production mechanisms, and a wide variety of subprocess cross sections. The results allow numerical predictions to be readily made for the cross sections of all these processes at the LHC and the Tevatron collider. For example, we predict that the cross section for the exclusive double-diffractive production of a 120 GeV Higgs boson at the LHC is about 3 fb, and that the QCD background in the bb decay mode is about 4 times smaller than the Higgs signal if the experimental missing-mass resolution is 1 GeV. For completeness we also discuss production via γγ or W W fusion.