  In a previous paper, we showed that many important quantum
information-theoretic phenomena, including the no-cloning and no-broadcasting
theorems, are in fact generic in all non-classical probabilistic theories. An
exception is teleportation, which most such theories do not support. In this
paper, we investigate which probabilistic theories, and more particularly,
which composite systems, {\em do} support a teleportation protocol. We isolate
a natural class of composite systems that we term {\em regular}, and establish
necessary and sufficient conditions for a regular tripartite system to support
a conclusive, or post-selected, teleportation protocol. We also establish a
sufficient condition for deterministic teleportation that yields a large supply
of theories, neither classical nor quantum, that support such a protocol.
