1. A method of operating network interface circuitry, wherein the network interface circuitry couples a host computer to a network to facilitate communication over the network between the host computer and a peer, the method comprising: by the network interface circuitry, receiving data from the peer via the network; and processing at least a portion of the received data, including: processing the at least a portion of the received data to determine an indication of a highest priority one of a plurality of actions to be performed by the network interface controller with respect to the received data, wherein the plurality of actions include filtering received data and protocol processing of received data for connections between the host and a peer for which the protocol processing has been offloaded to the network interface circuitry by the host, and the processing of the at least a portion of the received data includes presenting the at least a portion of the received data to lookup circuitry that is configured to automatically provide the indication of the highest priority action, associated with the received data, based not only on whether the portion of the received data presented to the lookup circuitry matches data associated with an indication of an action but also based on an order of the indications of the plurality of actions relative to each other in the lookup circuitry, the indications of protocol processing for connections that have been offloaded being located to indicate, when applicable to particular received data, a higher priority than the filtering actions; and performing the indicated highest priority one of the plurality of actions.