The possibility of superconductivity in doped and undoped triangular antiferromagnets is discussed. Using the Bethe-Salpeter (BS) equation, it is shown that the exchange of random-phase approximation paramagnons on a triangular lattice Hubbard model leads to strong pairing correlations at and near half filling. The dominant states for this system correspond to d-wave singlet (even-frequency) and s-wave triplet (odd-frequency) pairing. Analytical techniques applied to the hole-doped (Formula presented) model yield similar results. A (Formula presented) Hubbard model interpolating between square (Formula presented) and triangular (Formula presented) lattices has a tendency to only d-wave singlet pairing for (Formula presented) Experimental consequences for organic compounds (Formula presented) are discussed.