As a preparation for the study of arbitrary extensions of d = 2 gravity we present a detailed investigation of SO(N) supergravity. Induced d = 2, SO(N) supergravity is constructed by gauging a chiral, nilpotent subgroup of the OSp(N\2) Wess-Zumino-Witten model. In order to get a gauge-invariant theory with the correct number of degrees of freedom, we need to introduce N free fermions. From this we derive an all-order expression for the effective action. Reality of the coupling constant imposes the usual restrictions on c for N = 0 and 1. No such restrictions appear for N greater-than-or-equal-to 2. For N = 2, 3 and 4, no renormalizations of the coupling constant beyond one-loop occur. Also, in the effective N = 4 gravity based upon a linear N = 4 superconformal algebra, there is no renormalization at all, i.e. the quantum theory is equal to the classical. These results are related to non-renormalization theorems for theories with extended supersymmetries. Arbitrary (super)extensions of d = 2 gravity are then analyzed. The induced theory is represented by a WZW model for which a chiral, solvable group is gauged. From this, we obtain the effective action. All order expressions for both the coupling constant renormalization and the wave-function renormalization are given. From this we classify all extensions of d = 2 gravity for which the coupling constant gets at most a one-loop renormalization. As an application of the general strategy, N = 4 theories based on D(2, 1, alpha) and SU(1, 1\2), all WA gravities and the N = 2 W(n) models are treated in some detail.