1. A method of processing unexpected messages at a compute node of a parallel computer, the parallel computer comprising a plurality of compute nodes coupled for data communications via a data communication network, the method comprising: receiving, by the compute node, a portion of a message from another compute node of the parallel computer, the message comprising a plurality of separate portions; in response to receiving the portion of the message, determining, by the compute node, whether one of the applications executing on the compute node, has indicated that the message is expected; if one of the applications executing on the compute node has not indicated that the message is expected, storing, by the compute node, the portion of the message in an unexpected message buffer within the compute node; and if one of the applications executing on the compute node has indicated that the message is expected, storing, by the compute node, the portion of the message at a storage destination indicated by the message.