Number of times a table is read, written to and updated
In SQL Server Profiler, I tested this using SQL Server 2008. I don't know if the output will be the same in MSSQL 2000.

Using the template: TSQL_Replay


Select the Events Selection Tab
Check Show all events
Expand Performance then check Showplan XML
When you run your trace you will see the following events appear 




When you select Showplan XML, you will see the Execution plan generated by the query



If you hover your mouse over the Delete event, as in my example you will get the number of 
rows and other information related to the query

Update 15:50

Here is the SQL exported by profiler for the showplan XML event. 

exec sp_trace_setevent @TraceID, 122, 8, @on
exec sp_trace_setevent @TraceID, 122, 1, @on
exec sp_trace_setevent @TraceID, 122, 9, @on
exec sp_trace_setevent @TraceID, 122, 2, @on
exec sp_trace_setevent @TraceID, 122, 10, @on
exec sp_trace_setevent @TraceID, 122, 14, @on
exec sp_trace_setevent @TraceID, 122, 26, @on
exec sp_trace_setevent @TraceID, 122, 3, @on
exec sp_trace_setevent @TraceID, 122, 11, @on
exec sp_trace_setevent @TraceID, 122, 35, @on
exec sp_trace_setevent @TraceID, 122, 51, @on
exec sp_trace_setevent @TraceID, 122, 12, @on
exec sp_trace_setevent @TraceID, 122, 60, @on


122 is the event and then there is an id for each column selected in profiler for Showplan XML when I exported the trace to a file. 

Here is the list of events you can trace from Microsoft: Trace Events