Session types describe the structure of protocols from the point of view of each participating channel. In particular, the types describe the type of communicated values, and also the dynamic alternation of input and output actions on the same channel, by which a protocol can be statically verified. Crucial to any term language with session types is the notion of linearity, which guarantees that channels exhibit exactly the behaviour prescribed by their type. We relax the condition of linearity to that of affinity, by which channels exhibit at most the behaviour prescribed by their types. This more liberal setting allows us to incorporate an elegant error handling mechanism which simplifies and improves related works on exceptions. Moreover, our treatment does not affect the progress properties of the language: sessions never get stuck.