Finite-source images of earthquake rupture show that fault slip is spatially variable at all resolvable scales. In this study we develop scaling laws that account for this variability by measuring effective fault dimensions derived from the autocorrelation of the slip function for 31 published slip models of 18 earthquakes, 8 strike-slip events, and 10 dip-slip (reverse, normal, or oblique) events. We find that dip-slip events show self-similar scaling, but that scale invariance appears to break down for large strike-slip events for which slip increases with increasing fault length despite the saturation of rupture width. Combining our data with measurements from other studies, we find evidence for a nonlinear relationship between average displacement and fault length, in which displacement increases with fault length at a decreasing rate for large strike-slip events. This observation is inconsistent with pure width or length scaling for simple constant stress-drop models, but suggests that the finite seismogenic width of the fault zone exerts a strong influence on the displacement for very large strike-slip earthquakes.