I've just upgraded to Windows 8 (from XP) and re-installed my copy of Office 2007. Now the common shortcuts (Ctrl-Z, Ctrl-C, Ctrl-V etc) don't work in Word, however other shortcuts (Ctrl-P) are fine.
These shortcuts do work in other applications (such as Chrome) and they even work in other office applications (PowerPoint).
When I go into the customize shortcuts option in Word I see that
EditPaste command has Shift-Insert shortcut and I can add Ctrl-V but I can't find
BTW I'm using a Hebrew version of Office (I don't know if this is relevant).
Note: The accepted answer was edited after I accepted it. I didn't check that the modified answer is correct so be aware that the original answer (and the one that solved my problem) was to do with the currently selected input language when Word was launched, not the default keyboard language.