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The most influential civilisation in history is Poland 1919-1939 because it managed to maintain control of Vilnius despite the objections of Lithuania over the matter. The shocking, stunning Fall of Vilnius truly shook the world and put humanity into a slumber from which it never truly recovered.

Other less-influential-but-still-crucial world civilisations include the Soviet Union, the Russian Empire, Modern Lithuania, Poland-Lithuania and the Grand Duchy of Lithuania. If I were to narrow this list down to the top five as suggested by the OP I would put it something like this:
- Poland 1919-1939
- Modern Lithuania
- Poland-Lithuania
- Grand Duchy of Lithuania
- The Russian Empire

Soviets unfortunately for them are sixth (only just lower than the Russian Empire though) because they weren't as good at maintaining control of Vilnius as the others. Poland 1919-1939 obviously is at the top because they won the Vilnius Crisis, Modern Lithuania still maintains control of Vilnius today, Poland-Lithuania maintained control of Vilnius for centuries, the Grand Duchy of Lithuania actually made Vilnius, and the Russian Empire was also successful at maintaining control of Vilnius for quite a long time.
Good.
However even better if stripped of Lithuania.
 
Rome and China are the two Biggest IMO.

Afterward Great Britain with it establishing colonies across the globe settling What would become the USA today the current World power and 2 other economically large nations Canada Australia opening China up to the west in the opium wars India Africa 3 have to be in theirs.

This is gonna be much more recent but one nation that is largely responsible for the entire modern day is Germany WW1 and 2 changed the world with the Second ensuring the end of the Brtish Empire the French the fall of Japan the Rise of the USA and Soviet Union leading to the entire modern day situation.

The thing is we have to separate this into tiers there is no single 1 some nations had WAY more influence because of how expansive and large they are but some despite how small they have had a significant effect. Japan in terms of Nations are relatively small but have had a large effect on the history of the world.
 
Oh and you forgot to mention the ever fresh question of whether the T34 or the Panther tank were better.

Hey, we haven't had a really good T-34/Panther/Sherman debate for months!
 
Hey, we haven't had a really good T-34/Panther/Sherman debate for months!

Although I have to say such a debate would be extremely biased while no tanks of Polish or Lituanian (and probably Croatian) origin are included. Thus you could only award the title of the best non-Polish and non-Lithuanian tank. Which is quite a meaningless title.
 
Although I have to say such a debate would be extremely biased while no tanks of Polish or Lituanian (and probably Croatian) origin are included. Thus you could only award the title of the best non-Polish and non-Lithuanian tank. Which is quite a meaningless title.

Clearly this was the best WW2 tank:
800px-TKS_P1010141_2.jpg
 
Amongst the TOP 5 must be the Mongol Empire of Genghis Khan (and his successors). While not lasting very long time in one piece, it changed history of Eurasia, all the way from Silesia to Japan. They imposed Mongol rule over China. They destroyed muslim Caliphate, only renewed by Ottomans centuries afterwards. Mighty Khwarezmid Empire was wiped out along with it's cities and most of it's population.
Mighty Golden Horde, fought by Russians for generations or Tamerlane who destroyed Delhi and Baghdad (again), wouldn't happened as well. And that's just tip of the iceberg.
 
Amongst the TOP 5 must be the Mongol Empire of Genghis Khan (and his successors). While not lasting very long time in one piece, it changed history of Eurasia, all the way from Silesia to Japan. They imposed Mongol rule over China. They destroyed muslim Caliphate, only renewed by Ottomans centuries afterwards. Mighty Khwarezmid Empire was wiped out along with it's cities and most of it's population.
Mighty Golden Horde, fought by Russians for generations or Tamerlane who destroyed Delhi and Baghdad (again), wouldn't happened as well. And that's just tip of the iceberg.


And it inspired the finest ever of all the Eurovision entries.
 
No mention of the Empire of Man ?

Heretic ! It is indiscutably the one, greatest empire, the most influencal, and it reigned for millenias.
 
1 Roman Empire
2 Roman Republic
3 Eastern Roman Empire (Byzantine Empire)
4 Western Roman Empire
5 Roman Kingdom
 
The Hellenic "civilization" is a bit undervalued here imo. Also possibly the Frankish.