We show that the exact ground state wave function for an arbitrary two-body Hamiltonian can be exactly represented by a single reference coupled cluster wave function employing a general two-particle cluster operator. This can be used to construct a set of approximate methods that converge to the exact result and are in some sense complementary to the standard approach of including successively double, triple, quadruple, ..., excitations. We present exploratory variational results for the neon atom and the dissociation of N-2 to demonstrate the strengths and weaknesses of these generalized coupled cluster approximations.