  As a preparation for the study of {\it arbitrary} extensions of $d=2$ gravity
we present a detailed investigation of $SO(N)$ supergravity. By gauging a
chiral, nilpotent subgroup of the $OSp(N|2)$ Wess-Zumino-Witten model we obtain
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 $N\geq 2$. For $N=2$, 3 and 4, no renormalizations of
the coupling constant beyond one loop occur. 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 wavefunction 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 $D(2,1,\a)$ and $SU(1,1|2)$, all
$WA$ gravities and the $N=2$ $W_n$ models are treated in some detail.
