I've seen this topic a few times in various corners of the web, but it usually boils down to one or two people getting ridiculed by a dozen others for suggesting New York or London. So as I'm on a long, lazy holiday I thought I'd try it myself, with a few pointers to make the topic a little less vague & subjective.
Pointers:
* History is a long time. That means that a young city, even one of earth shattering importance right now, will have to compete with candidates that have had a more subtle influence for two thousand years or more.
* Candidates have to stand out on their own merits, not simply because a famous event happened around them or they happened to be the capital of a powerful nation.
Example one; Stalingrad was the scene of a historically pivotal battle, but the character of the city itself had little or nothing to do with it. Jerusalem has also been at the centre of a few major battles in its time, but in those cases the character of the city itself was most definitely central.
Example two; Washington DC draws its influence from being designated the capital of the USA. Had the seat of power been situated elsewhere in America the wider historical outcome may not have been remarkably different. Rome, on the other hand, created & --- for a time at least --- remained at the heart of its wider empire.
Example three; India's influence of world affairs as been spread evenly through many cities over the millennia. Therefore it is bound to be underrepresented due to a lack of an urban focal point.
* I found myself putting them in three different levels for convenience. I haven't ordered them within these levels.
A-listers are those with a damn good chance of getting to the top spot.
B-listers are those with an outside chance; those for which a reasonably convincing case could probably be made.
C-listers are those without any real chance at being the most influential city in history, but which are very influential in specific areas nonetheless. This is so broad that it's bound to be able to contain hundreds of cities with wildly different degrees of influence (see Mecca & LA).
Without further ado, here's my start. Please suggest your own (or disagree violently with me, if you like).
A-listers:
Jerusalem --- Most important city in religious history, seldom out of the spotlight for thousands of years.
Athens --- Birthplace of Western civilization (no Ghandi jokes, please). Hugely influential in the fields of philosophy, what stood-in for science for a long time, politics & general free thinking, not to mention playing a pivotal role in keeping Persia at bay for a millennia.
Peking/Beijing --- Whilst at the heart of China for thousands of years, Beijing has been pivotal in sustaining a uniquely politically, linguistically & culturally unified ancient civilisation, China. [--- Edit: see JBI's comment below]
Rome --- Still the touchstone for measuring imperial power, cultural worth & technological progress through Europe & beyond. Also the originator of 'civil law', amongst other things, & the home of Catholicism.
Eridu --- The world's first city, formed when fishermen, peasants & nomads settled down together in the first major settlement in human history. Although the city concept was later independently 'invented' in China, Mexico & possibly Egypt, had Eridu not worked out perhaps the whole of civilised history would have been set back a thousand years or more.
B-listers:
Babylon --- Capital of numerous Fertile Crescent cultures, possibly even founded by Sargon the Great, history's first 'Emperor'. But Babylon would get in the list by weight of cultural references alone. Not only has its character become shorthand for decadence & oppression, but it was one such moment of oppression --- when the exiled Jews were first introduced to grand, urban civilisation --- that lead to the birth of truly monotheistic Judaism.
London --- The permanent nexus of the British Empire for over three hundred years, bringing more disparate parts of the world into the 'European age' & Anglosphere than any other city. Home of the Royal Society, midwife to modern science, & the so-called Mother of Parliaments. Also the original 'megacity'. London today is one of only two cities (New York being the other) considered completely pivotal to the modern economy.
Paris --- The centre of European culture & intrigue since the middle ages. Paris embodied & influenced Europe like no other through-out the 'European age', & remains the final arbitrator of the only centrally managed world language. Finally, events in Paris during the French Revolution shook the social & political of the world in ways that are hard to exaggerate.
Byzantium/Constantinople/Istanbul --- The conduit between Asia & Europe. Instrumental in the spread of Christianity, the maintenance of Roman culture, initially checking of Muslim ambitions in Europe, then the centre of the massive Ottoman empire.
C-listers:
Mecca --- Not a B-lister for the simple reason that its main influence is through religion, a field in which it is overshadowed by Jerusalem. In other fields, such as politics & culture, it was eventually replaced by Baghdad within the Muslim world, but not before it had dramatically reshaped the region. As the world's most popular site of pilgrimage is remains influential to this day.
New Amsterdam/New York --- New York has lead America's surge to the forefront of the world stage over the past century & is also considered symbolic of America generally. It is the only other city (with London) considered completely pivotal to the modern economy. If the pattern continues for another century or more, New York will almost certainly be a B-lister, but has currently only been influential for a very short time.
Los Angeles --- First example of a city explosively broadcasting its culture over the entire world. No other has had the same cultural impact in so short a time.
Alexandria --- Symbolising the joining of Hellenic & Egyptian cultures, not to mention the preciousness of knowledge. Continued to be a lightning rod for Egyptophilia well into the Victorian era.
Moscow --- A seat of largely uninterrupted political power for centuries. As the Russian transitions from nomadic barbarism to Tsarism, from Tsarism to Communism, & from Communism to a free-market bear pit all hinged on events in this city, Moscow has played out many of the most dramatic social & political changes anywhere.
Oxford --- Home of one of the oldest & most influential seats of learning in the world. Still the model for all other Anglophone University towns, particularly Cambridge & the other Cambridge. Men & women trained in Oxford & its imitators continue to dominate national & international institutions, including an inordinate number of Heads of various states.
Unknown (those about which I don't know enough to speculate but suspect desirve a place in A, B or C):
Baghdad ---
Cairo ---
Shanghai ---
Hong Kong ---
Vienna ---
Tokyo ---
Madrid ---
Antioc ---
Tenochtitlan/Mexico City ---
Timbuktu ---
Ur ---
Berlin ---
Delhi ---
Kakamuchee/Bombay/Mumbai ---
What do you reckon?