Most influential and important Popes of all 21 centuries of Church history:
1st century:
St. Pope Peter the Apostle
St. Pope Linus the Second
St. Pope Clement I
2nd century:
St. Pope Victor I
St. Pope Zephyrinus
3rd century:
St. Pope Pontian
St. Pope Marcellinus
4th century:
St. Pope Sylvester I
St. Pope Mark
St. Pope Damasus I
5th century:
St. Pope Leo I, the Great
St. Pope Gelasius I
6th century:
St. Pope Hormisdas
St. Pope Gregory I, the Great, the Dialogues
7th century:
St. Pope Adeodatus I
St. Pope Martin I
St. Pope Sergius I
8th century:
St. Pope Leo III
9th century:
St. Pope Paschal I
St. Pope Nicholas the Great
10th century - the first century where we don’t find any canonized Popes, in fact there aren’t even any Beati or even Servants of God. The 10th century is also when the Medieval Papacy is beginning to come to its peak of temporal power, where it will remain for the next 6 or 7 centuries. The most influential in the 10th, IMO:
Pope Leo V
Pope John X
Pope John XII
Pope Benedict V
11th century:
St. Pope Leo IX
St. Pope Gregory VII
Blessed (Bl.) Pope Urban II
12th century:
Bl. Pope Eugene III
13th century:
Bl. Pope Gregory X
Bl. Pope Innocent V
St. Pope Celestine V
14th century:
Bl. Pope Benedict XI
Pope Clement V
Bl. Pope Urban V
15th century (the second century with no canonised Pontiffs):
Pope Alexander VI
Pope Innocent VIII
16th century:
Pope Leo X
St. Pope Pius V
Pope Gregory XIII
17th century:
Bl. Pope Innocent XI
Pope Clement X
18th century (third and latest/last century with no Saints or Beati or even Venerables, only one Servant of God):
Servant of God (S.D.) Pope Benedict XIII
Pope Clement XIII
19th century:
S.D. Pope Pius VII
Pope Pius VIII
Bl. Pope Pius IX (first Pope to ever be photographed, which was quite controversial in that day and age for a Pope)
Pope Leo XIII (who IMO should be a Saint, but as far as I’m aware any potential cause for his canonisation is stalled).
20th century:
St. Pope Pius X
Pope Benedict XV
Venerable (Ven.) Pope Pius XII
St. Pope John XXIII
St. Pope Paul VI
Ven. Pope John Paul I
20th/21st centuries:
St. Pope John Paul II, the Great (the latest and fourth Roman Pontiff to bear the moniker ‘the Great’).
And of course our saintly and beloved Pope Emeritus Benedict XVI, and our beloved and saintly reigning Roman Pontiff Pope Francis.
I spent a good deal of time and effort compiling this, I hope it is helpful or interesting to some.