My ultimate question is embodied in the title but I thought it might be helpful to others if I detail what instigated my inquiry and my examination of the problem.

To me, the first rule of software updates is Primum non nocere -- first, do no harm. So with my Windows 7 system containing both Office 2003 and Office 2010 I blithely proceeded to install this month's updates from Microsoft, containing updates for both versions of Office. While Microsoft officially does not recommend running multiple versions (see, for example, Running Multiple Versions of Microsoft Excel it is possible; I have had two versions installed for a year or more and have never run into an issue before. One thing that is always mentioned is installation order, i.e., the one you want to open files by default should be installed last. I wanted 2010 as my default so I had indeed installed 2003 first then, years later, 2010. So with this round of Windows updates, either it installed patches to 2010 before 2003, knocking out the file association, or the 2003 patch was more comprehensive, in the sense of touching the file association while the 2010 did not. In any case, after updates, double-clicking a .xls file opened 2003 rather than 2010.

Web search indicated either:

1. Use the file associations control panel to re-associate .xls files with the correct version of excel. I looked at this first, but it showed what seemed to be an unversioned "Excel" associated with .xls files so I did not check further. (This turned out to be an error on my part; more later.)
2. Re-install versions in the desired order; I find this unreasonable.
3. Run the repair option of the Office installer on the desired version; still seems more work than one should need.
4. Run excel from the command line with "/regserver" on the one to be the default and "/unregserver" on the other. Good idea, but further search indicated that neither 2007 nor 2010 support "/regserver" contrary to some posts (e.g. Default Program With Multiple Versions Installed).

Since this was a Windows Update issue and Microsoft provides free support for such, I inquired there as well, but succeeded only in getting the suggestion to uninstall all other versions, period; not acceptable to me.

What worked for me was going back to the file associations control panel and manually selected the Office 2010 version of Excel. While it appeared no different in the control panel, it did fix the double-click issue. So if all it takes is this simple fix after an update, I can live with that. What I am wondering is: Has anyone seen any other problems related to having multiple versions of Office installed?