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The varieties of leaky waves supported by planar multi-layered structures are determined for the general case of an arbitrarily stratified layer placed between a substrate and a superstrate. For lossless media in the substrate and superstrate, but for either lossy or lossless layers, a total of eight different leaky-wave fields are found. These various types of leaky waves are distinguished by forward or backward traveling characteristics on the one hand, and by similar (co-leaky) or different (contra-leaky) power-flow behavior in the two exterior regions on the other hand. The co-leaky waves can exist if the superstrate and substrate consist of either the same or different media, but the contra-leaky waves appear only if these media are different. By investigating the field generated by realistic sources, it is shown that only four out of the eight leaky-wave varieties can be excited so that the other four should have little physical significance. However, the excitable four types of leaky waves can be strongly generated by suitable sources, and three of them have already found interesting applications in the coupling of beams into (or out of) layered structures and in the guiding of plasmon waves by thin metal films.