1. A machine-implemented method for sharing state information among a plurality of servers, comprising: receiving, from a particular client at a first server of the plurality of servers, a request to perform a network file system (NFS) operation; in response to receiving the request to perform the NFS operation, updating first state information, stored at the first server, to reflect a change in state associated with processing the request, wherein said state information specifies an operational state of the file, wherein said operational state reflects one or more stateful operations previously performed on said file by said requester; propagating, from the first server to a second server of the plurality of servers, state update information that identifies the change in state; based on the state update information that identifies the change in state, updating second state information, stored at the second server, to reflect the change in state associated with processing the request at the first server, wherein said second state information specifies said operational state of the file; said second server receiving a second request, from a client, to perform a second NFS operation, wherein said client transmitted said request to said first server; and said second server using said state information that was propagated to said second server from the first server to determine how to service said second request; wherein the step of propagating the state update information comprises: determining a priority associated with said change in state; upon determining that said change in state has a first priority, performing the steps of: the first server durably storing information identifying said change in state to a persistent storage, and the second server reading the information identifying said change in state the persistent storage; and upon determining that said change in state has a second priority, performing the step of: transmitting, from a first volatile memory at the first server to a second volatile memory at the second server, information identifying said change in state.