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This problem is addressed in ArcGIS 8.1 Service Pack 1. See Related Information section to download this pack.
Summarize field in ArcMap causes this error:
Untitled - ArcMap - ArcInfo: ArcMap.exe - Application Error.
The instruction at "0x0ef456fe" referenced memory at "0x0000000000". The memory could not be "read".
Click on OK to terminate the program.
Click on CANCEL to debug the program.
This occurs if you try and summarize a join table after adding a field to it.
Add the field prior to the join.