UPDATE: 10 March 2015: Microsoft have now released fixes for this!
For Excel 2007 click here.
For Excel 2010 click here.
For Office 2013 click here. (note there doesn’t appear to be a separate Excel patch)
Note: I have not actually been able to verify whether these patches work, but some early reports suggest they don’t work for everyone (perhaps for the same reason that the fixes below didn’t).
I am also unsure at this time as to whether Office 2003 was affected, but have not seen any mention of a patch if it was.
Update: 15 Dec 2014: There is now an MSKB article about this problem with suggested solutions and a FixIt tool here: KB3025036.
It seems that a recent Office update (Tuesday 9th Dec) has broken ActiveX controls on worksheets. The symptoms include (but are probably not limited to):
- Being unable to use or change properties of any active controls on worksheets
- Error messages saying “Can’t insert object”
- Error 438 when trying to refer to an activex control as a member of a worksheet in code
To fix it, do this:
- Close all Office applications.
- Do a search in Windows Explorer – make sure to include hidden and system files and folders – for *.exd files (note: that’s not *.exe !!) and delete any you find.
Make sure you get these:
C:\users\username\AppData\Local\Temp\Excel8.0\MSForms.exd
C:\users\username\AppData\Local\Temp\VBE\MSForms.exd - Reboot the computer (this is not always necessary, but probably better safe than sorry)
- Restart your Office apps and test the controls again.
Please note that the .exd files will be recreated when you next use a workbook with an embedded active control – this is quite normal and should not cause you a problem!
Hopefully that will resolve the problem for you. 
Note: if you are having problems locating the .exd files, you can press Win+R to open the Run box, enter %temp% and press Enter. That should open explorer to the Temp folder and you then need to look in the Excel8.0 and VBE folders for the .exd files. (if your issue is with a program other than Excel, look for the folder related to that application – e.g. Word8.0)
Update: 11-Dec: It seems that for a few cases so far, this solution doesn’t resolve the issue. I will post back if and when I discover a solution for those cases too, though simply uninstalling the update mentioned at the beginning of this post may be a solution until a fix is released.
Trust me, Microsoft is aware that this is an issue – see their blog post here.
Update: 12 Dec 2014: I have seen mentions that if none of the above fixes the issue in Office 2013, removing this update may work: http://support.microsoft.com/kb/2920734