We study globular cluster evolution using Hénon's Fokker-Planck equation to model relaxation and energy exchange between the stars. We include a spectrum of stellar masses, stellar evolution, and accompanying mass loss, and a tidal boundary determined by cluster mass and Galactocentric position. All these features are important for modeling cluster evolution until the onset of core collapse. We present a comprehensive survey of Galactic globular cluster evolution until core collapse. Mass loss during the first 5 × 109 yr is sufficiently strong to disrupt weakly bound clusters with a Salpeter initial mass function (IMF). The slope of the IMF is the critical parameter governing cluster survival during the mass-loss phase. Clusters which survive this initial phase then begin to collapse. Those with smaller mass and/or smaller Galactocentric orbital radii complete their core collapse by the present time. Energy input from stellar evolution and the decrease in the range of the mass spectrum delay the onset of core-collapse times for all clusters. Many clusters from a plausible set of initial conditions are heading toward their first collapse today. We investigate two evolutionary endpoints in detail: (1) the disruption of weakly bound clusters by mass loss due to stellar evolution; (2) core collapse of multimass clusters. We analyze the endpoint of collapse of multimass stellar models and show that the power-law homology, so evident in single-component studies, is not as useful in the more realistic simulations. Finally, we discuss the state in which the multimass clusters find themselves today, if they have neither disrupted nor collapsed. We present a number of observables (colors, surface brightness, mass-to-light ratios, and mass functions) based on stellar evolution calculations. Surface brightness profiles appear to be insensitive to the dynamical state of the cluster. In particular, the luminous component does not trace the extreme cusp; King models give adequate fits to the predicted photometry, even in collapse. Mass segregation leads to only weak color gradients. However, the radial variation of the mass function will be a useful diagnostic of the dynamical state of a cluster and, indirectly, of a cluster's evolutionary history.
