The most general gravitational lagrangian which can be constructed from the curvature two-form, the vielbein one-form, and tensors invariant in the tangent space is a linear combination of dimensionally extended Euler characteristics. Several recent studies indicate that superstring lagrangians include such terms. In an arbitrary number of dimensions, with arbitrary torsion, we show that in the most general such extended theory the only static, spherically symmetric, massive solutions to the variational equations of motion contain gravitational singularities. The existence of an event horizon is proved for certain cases, and a bound on the location of singularities is found. A certain class of non-asymptotically flat solutions is found for which the metric and the torsion are not entirely determined by the field equations.