[Faceman]

There are several founding myths about Rome. The official one was the Romulus-Remus story.
Another extremely popular myth considered Rome to be founded by Aeneas the Trojan hero who survived and fled Troy to rebuild its heritage.
Later on these myths were synchronized and Aeneas son Ascanius (a.k.a. Iulus) was named as the founder of Alba Longa and its line of kings, which Romulus and Remus originated from.

But onto the historic question. It was a lot easier to keep up a big empire back then, because the idea of Nationalism was not fully developed and not very widespread. Rome was the superior military and (after beating Carthago) mercantile power of the mediterranean area. They did not interfere with the religion of the captured peoples and brought them organized government. Don't forget, that if your living in an authoritarian system anyway (as was the rule back then) there is not much point in overthrowing your new rulers, just because they are outsiders. Politics and empires were not formed by the people back then, Greeks were Egypt Pharaos, Phoenicians ruled Mauretania and Spain and the Romans just took over the whole mediterranean because they played this power-game most professionally.