  We classify all N=2 rigid supersymmetric backgrounds in four dimensions with
both Lorentzian and Euclidean signature that preserve eight real supercharges,
up to discrete identifications. Among the backgrounds we find specific warpings
of S^3 x R and AdS_3 x R, AdS_2 x S^2 and H^2 x S^2 with generic radii, and
some more exotic geometries. We provide the generic two-derivative rigid vector
and hypermultiplet actions and analyze the conditions imposed on the special
Kahler and hyperkahler target spaces.
