The effective action of d=4, N=2 supergravity is shown to acquire no quantum corrections in background metrics admitting supercovariantly constant spinors. In particular, these metrics include the Robinson-Bertotti metric (product of two two-dimensional spaces of constant curvature) with all eight supersymmetries unbroken. Another example is a set of arbitrary number of extreme Reissner-Nodström black holes break four of eight supersymmetries, leaving the other four unbroken. We have found manifestly supersymmetric black holes, which are non-trivial solutions of the flatness condition D2=0 of the corresponding (shortened) superspace. Their bosonic part describes a set of extreme Reissner-Nordström black hole solutions are exact even when all quantum supergravity corrections are taken into account.On leave of absence from Lebedev Physical Institute, 117 924 Moscow, USSR.