There is no simple answer to this question. General relativity does not generically have any way to define the total energy of a system; it only has conserved, scalar measures of the total energy of a system in particular special cases, such as asymptotically flat spacetimes. Even then, there is more than one such measure of energy. For instance, we have the ADM energy and Bondi energy, both of which are conserved for an asymptotically flat spacetime. They differ because the Bondi energy doesn't include energy being radiated away to infinity by gravitational waves, whereas the ADM energy does.
Note also that these energies are not additive as in Newtonian mechanics.
The basic reason for all of this complication is that the equivalence principle says that the gravitational "field" in the Newtonian sense is unobservable. A free-falling observer (which is the preferred kind of inertial observer in GR) always measures the gravitational field to be zero. Therefore we can't have, as we do in Newtonian mechanics, an equation that defines the energy density in terms of the gravitational field. When relativists talk about the "gravitational field," they really mean the curvature, not the meaningless Newtonian $g$.
There seems to have been a lot of dispute and confusion in comments and answers about whether the energy in the gravitational field is positive or negative. Well, in general, it's not even defined, but in the cases where it's defined, it can be either positive or negative. For example, a Schwarzschild black hole has a positive ADM energy, which is equal to its inertial mass, and this energy is entirely due to its gravitational field (since it's a vacuum solution to the Einstein field equations, i.e., no matter is present). On the other hand, the gravitational energy of the earth is certainly negative, because the earth is nonrelativistic, and in the nonrelativistic approximation energy is additive and gravitational energies are negative. Gravitational waves have positive energy.