We present predictions on the total cross sections and on the rho parameter for present and future pp and (-)pp colliders, and on total cross sections for gammap-->hadrons at cosmic-ray energies and for gammagamma-->hadrons up to sqrt[s]=1 TeV. These predictions are based on an extensive study of possible analytic parametrizations invoking the largest hadronic dataset available at t=0. The uncertainties on total cross sections reach 1.9% at the Relativistic Heavy Ion Collider, 3.1% at the Tevatron, and 4.8% at the Large Hadron Collider, whereas those on the rho parameter are, respectively, 5.4%, 5.2%, and 5.4%.