We report extensive laser-induced damage threshold measurements on dielectric materials at wavelengths of 1053 and 526 nm for pulse durations τ ranging from 140 fs to 1 ns. Qualitative differences in the morphology of damage and a departure from the diffusion-dominated τ 1 2 scaling of the damage fluence indicate that damage occurs from ablation for τ<~ 10 ps and from conventional melting, boiling, and fracture for τ> 50 ps. We find a decreasing threshold fluence associated with a gradual transition from the long-pulse, thermally dominated regime to an ablative regime dominated by collisional and multiphoton ionization, and plasma formation. A theoretical model based on electron production via multiphoton ionization, Joule heating, and collisional (avalanche) ionization is in quantitative agreement with the experimental results.