  We prove that a generalized Schwarzschild-like ansatz can be consistently
employed to construct $d$-dimensional static vacuum black hole solutions in any
metric theory of gravity for which the Lagrangian is a scalar invariant
constructed from the Riemann tensor and its covariant derivatives of arbitrary
order. Namely, we show that, apart from containing two arbitrary functions
$a(r)$ and $f(r)$ (essentially, the $g_{tt}$ and $g_{rr}$ components), in any
such theory the line-element may admit as a base space {\em any}
isotropy-irreducible homogeneous space. Technically, this ensures that the
field equations generically reduce to two ODEs for $a(r)$ and $f(r)$, and
dramatically enlarges the space of black hole solutions and permitted horizon
geometries for the considered theories. We then exemplify our results in
concrete contexts by constructing solutions in particular theories such as
Gauss-Bonnet, quadratic, $F(R)$ and $F$(Lovelock) gravity, and certain
conformal gravities.
