What does it mean when I see a value of 1900-01-01 00:00:00.000 in master..sysprocesses' last_batch column?

The last_batch name is misleading. The term batch in SQL Server refers to a batch of SQL statements that's sent to the server and is received by either the SQL listener or the remote procedure call (RPC) listener. The first type has a SQL:BatchCompleted event class in SQL Server Profiler, whereas the second type has a RPC:BatchCompleted event class. However, SQL Server Books Online (BOL) says that the definition of last_batch in master..sysprocesses is the "last time a client process executed a remote stored procedure call or an EXECUTE statement. For system processes, the time at which SQL Server startup occurred is stored." That definition seems to mean that the value for last_batch isn't updated when a SQL:BatchCompleted event happens. But that's not true—the value will be updated when a SQL:BatchCompleted event happens. However, the value will never be set if a given connection doesn't execute at least one RPC:BatchCompleted event on the connection. Most clients issue at least one RPC call during the connection process. However, it's possible to create a connection to SQL Server without issuing any RPC calls at all. In this case, the value of last_batch will never have been set and master..sysprocesses will display the value as 1900-01-01 00:00:00.000. This behavior is discussed in more detail in the Microsoft article "INF: Last Batch Date is Seen as 1900-01-01 00:00:00.000" at http://support.microsoft.com/?kbid=306625.