Information on the time intervals between large earthquakes is now available for several fault segments along plate boundaries in Japan, Alaska, California, Cascadia, and Turkey. When dates in a sequence are known historically, as along much of the Nankai trough, they provide information on the natural (intrinsic) variability of the rupture process. Most sets of repeat times, however, are dominated by paleoseismic determinations of dates of older large earthquakes, which contain measurement uncertainties in addition to intrinsic variability. A Bayesian technique along with prior information on measurement uncertainties is used to make maximum-likelihood estimates of intrinsic repeat time and its normalized standard deviation, the coefficient of variation (cv). It is these intrinsic parameters and their uncertainties that are most useful for understanding the mechanics of earthquakes and for prediction for timescales of a few decades. Our estimates of intrinsic cv are small, 0 to 0.25, for several very active fault segments where deformation is relatively simple, large events do not appear to be missing in historic and paleoseismic records, and data are available at or near major asperities and away from the ends of rupture zones. cv is larger for regions of multibranched faulting, overlapping slip near the ends of rupture zones and for data from uplifted terraces at subduction zones. A Poisson process is an inferior characterization of all of the 11 segments we examined. Scenarios used by recent working groups that assume either Poissonian behavior or renewal processes with cv of 0.5 ± 0.2 for the most active fault segments in the San Francisco Bay area likely lead to incorrect 30-year probability estimates. The Hayward fault and perhaps the Peninsular segment of the San Andreas fault in the San Francisco Bay area appear to be advanced in their buildup of stress that will be released in future large earthquakes. Multibranched faulting may account for why the predicted Tokai earthquake in Japan has not occurred as of 2006. Parkfield earthquakes from 1857 to 2004 were characterized by the largest uncertainty of the sequences we studied, cv = 0.37, which may account for the failure of past predictions. The large cv for Parkfield fits our hypothesis that relatively weak fault segments are characterized by more irregular earthquake recurrence. Paleoseismic data from coastal sites along the Cascadia subduction zone are characterized by cvs of about 0.3.