Everybody's got 2...
Harv 6--IMHO (There we go right off the bat, with an OPINION!) Opinions is all you'll ever get on this subject. I see ratings based on the # of a given cartridge of reloading dies sold, but that limits it to people who reload (and who buy the particular makers' dies.) # of rifles sold, you'd have to get that from each of the manufacturers, and I doubt that you'd get complete information from all of them. Likewise volumes of ammunition of any given cartridge sold.
There are probably opinions on this to be found in various gun related magazines, too, based on whatever criteria the writer was using for that particular article.
I suspect that there's a doctorate or 2 to be had, in the finding out of the most popular cartridges, but (a) it'd take years of study and (b) many bucks in grants to find it all out, and sift and evaluate and publish the data. And whatever was discovered would immediately be challenged, that being the way of academia.
I'm pretty certain myself, that at the A#1 top of any list except centerfires only, you would find the lowly and ubiquitous .22 Long Rifle cartridge.
Other than that, there probably is no definitive listing. If you find one, please let us all know!
Good hunting!