score:6
As near as I can tell, the only western country (for some definitions of "western") that was directly involved in a war in early 2001 was Russia in the Second Chechen War.
Israel, if you count them, was dealing with the Second Intifada. Roughly on that level there was an ethnic Albanian insurgency in Macedonia.
That is certainly a low ebb. The number of conflicts per year has been more or less on the rise since, with a particular spike up in 2012.