This is possible with a macro, but each user that accesses the sheet
would either have to have their macro security setting set to low, or
they would have to open the workbook with macros enabled.

XL is not a secure environment for storing sensitive data. You can lock down
sheets using passwords including (xl2002 or better) allowing only certain
users to edit certain ranges. That being said passwords can be hacked in XL
quite easily.

You can check to see who the last person to access an XL file was (even if
they did not save the file) using a text editor. That is not something that
most people are willing to do.