SelectionChange is the event built into the Excel Object model for this. It should do exactly as you want, firing any time the user clicks anywhere...
I'm not sure that I understand your objections to global variables here, you would only need 1 if you use the Application.SelectionChange event. However, you wouldn't need any if you utilize the Workbook class code behind (to trap the Workbook.SelectionChange event) or the Worksheet class code behind (to trap the Worksheet.SelectionChange) event. (Unless your issue is the "global variable reset" problem in VBA, for which there is only one solution: error handling everywhere. Do not allow any unhandled errors, instead log them and/or "soft-report" an error as a message box to the user.)
You might also need to trap the Worksheet.Activate() and Worksheet.Deactivate() events (or the equivalent in the Workbook class) and/or the Workbook.Activate and Workbook.Deactivate() events so that you know when the user has switched worksheets and/or workbooks. The Window activate and deactivate events should make this approach complete. They could all call the same exact procedure, however, they all denote the same thing: the user changed the "focus", if you will.
If you don't like VBA, btw, you can do the same using VB.NET or C#.
[Edit: Dbb makes a very good point about the SelectionChange event not picking up a click when the user clicks within the currently selected cell. If you need to pick that up, then you would need to use subclassing.]