Progress in the field of superconductivity is often linked to the discovery of new classes of materials, with the layered copper oxides being a particularly impressive example. The superconductors known today include a wide spectrum of materials, ranging in complexity from simple elemental metals, to alloys and binary compounds of metals, to multi-component compounds of metals and chalcogens or metalloids, doped fullerenes and organic charge-transfer salts. Here we present a new class of superconductors: insulating organic molecular crystals that are made metallic through charge injection. The first examples are pentacene, tetracene and anthracene, the last having the highest transition temperature, at 4 K. We anticipate that many other organic molecular crystals can also be made superconducting by this method, which will lead to surprising findings in the vast composition space of molecular crystals.