  The entropy of black holes in modified theories of gravity is examined in the
Palatini formalism using the Noether Charge approach. It is shown that, if the
gravitational coupling constant is properly identified, the entropy of a black
hole is one-quarter of the horizon area in f(R) theories coupled to conformally
invariant matter. If matter is present that is not conformally invariant the
entropy is still proportional to the area of the black hole, but the
coefficient is generally not one-quarter. The entropy of black holes in
generalized dilaton theories and in theories with Lagrangians that depend on an
arbitrary function of the Ricci tensor are also examined.
