  We study finite-dimensional extra symmetries of generic 2D dilaton gravity
models. Using a non-linear sigma model formulation we show that the unique
theories admitting an extra (conformal) symmetry are the models with an
exponential potential $V \propto e^{\beta\phi}$ ($ S ={1\over2\pi} \int d^2 x
\sqrt{-g} [ R \phi + 4 \lambda^2 e^{\beta\phi} ]$), which include the CGHS
model as a particular though limiting ($\beta=0$) case. These models give rise
to black hole solutions with a mass-dependent temperature. The underlying extra
symmetry can be maintained in a natural way in the one-loop effective action,
thus implying the exact solubility of the semiclassical theory including
back-reaction. Moreover, we also introduce three different classes of
(non-conformal) transformations which are extra symmetries for generic 2D
dilaton gravity models. Special linear combinations of these transformations
turn out to be the (conformal) symmetries of the CGHS and $V \propto
e^{\beta\phi}$ models. We show that one of the non-conformal extra symmetries
can be converted into a conformal one by means of adequate field redefinitions
involving the metric and the derivatives of the dilaton. Finally, by expressing
the Polyakov-Liouville effective action in terms of an invariant metric, we are
able to provide semiclassical models which are also invariant. This generalizes
the solvable semiclassical model of Bose, Parker and Peleg (BPP) for a generic
2D dilaton gravity model.
