London has remained a center of cultural activity for more than a thousand years, and it still originates many of the trends found in modern society (the fashion world, for example). It was the city which stood alone as a symbol for freedom during World War II, and its important historical legacy can still be found in the millions of tourists which visit each year.
I have always been intrigued by both Rome and Egypt. The great culture and influence each have on modern day society are endless. While I am sure others have their opinions on which are important, I do think that everyone will have his or her own idea as to why.
Jerusalem has clearly been an important city since Roman times, as a sacred location for three of the world's major religions. Another important city was Byzantium/Constantinople/Istanbul, which served as a major cultural, political, and commercial link between Europe and the Near East for centuries. I can't disagree with any of the options offered by other posters, but one slightly less than orthodox choice might be Cahokia, which served as a major cultural and political center of North America for several hundred years before its decline. Some historians and archaeologists, most recently Timothy Pauketat, have argued that its political and cultural influence extended from modern Canada to Florida to the Great Plains.
I think it is difficult to compare such different cultures and say which is more important. All of these cities were influential in developing the regions around them in their own way. Just because one had more influence on the Western World, does that make it more important?
Paris has played an important cultural and political role in world history in the last few hundred years. With the uprising of democracy in the 1700s, the subsequent rise and fall of Napoleon, and the development of a great and egalitarian arts culture, Paris has seen its share of important and influential moments.
Rome has to be #1 on the list, at least in the West. Since Rome was the center of the Roman Empire, and since the Roman Empire did so much to create Europe as we know it today, I would say it's Rome.