The question is actually invalid, because both Essendon and Carlton have won the most at 16 premierships each. Therefore, the next team will have won the third most AFL Premierships; and that is Collingwood. The Collingwood Magpies have won 15, but they have lost many more grand finals than they have won!
Essendon and Carlton: having each won 16/114 contested have the highest percentage of premierhips won, having been in the competition from the beginning.
Collingwood, which has also been in the competition from the beginning, has won 15/114 that have been contested ... and Melbourne 12/114.
So those 4 clubs, among them, have won well over half of all the premierhips so far contested.
Essendon and Carlton have won the most premierships with 16 premierships each.
Carlton and Essendon who have won 16 premierships each.
Collingwood has played in 43 grand finals (including 2 draws). This is the VFL/AFL record.
Essendon has winning 130 grand finals
Carlton & Essendon
Which AFL team has won 10 premierships
During the 1950's and 1960's, Norm Smith coached the Melbourne Football Club to 6 Premierships over 11 seasons, with 11 consecutive finals appearances! Those were the days when only 4 teams made the finals. None other has even approached that kind of record.