Several of the posted answers to the question bring up good points, but those same answers appear to be aspects of the central explanation. I would submit that the answer to Roman success was not anything intrinsic to the mechanics of empire as much as a cultural phenomena. To cut to the quick, I believe there were two distinct features that combined to give Rome its dominance: discipline and pragmaticism.
A simple illustration of discipline: in 216 B.C. Rome suffered the worst defeat in its history. Cannae saw the Roman leadership decimated, some possible 60,000 dead on the field and Hannibal free to march on Rome (taken as a proportion of loss to available resources at the time, I can think of few possible worse disasters). The victorius Carthaginians sent envoys to Rome to ask for terms. The Roman response was basically how would Hannible like to surrender? The bravado behind that sentiment is stunning. I can think of no other nation or people who could have recovered. This is but one example of a sentiment that is illustarted over several Centuries.
Roman pragmaticism is evident in everything from road construction, to citizen mobilization, to adopting the gladius, to the construction of the corvus, to the development of a counter to the phalanx. Unlike the Greeks, Rome never produced an independant intellectual system. Their ability to focus on the task at hand and develope a proper response however, is stunning. This feature allowed Rome to create the longest sustained Empire in history.
These two cultural traits allowed Rome the wherewithal to overcome any opposition. It would be the dilution of these same traits that would sow the seed of Rome's decline.
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