This image here: http://upload.wikimedia.org/wikipedia/commons/0/00/Roman_Empire_Trajan_117AD.png

Shows Rome at its greatest extent in 117AD under the Emperor Trajan.

Given that the city of Rome was established around 750BC it took them 867 years from their founding to achieve this massive empire.

It should also be noted that Rome only became the dominant power in Italy in 290BC when it defeated the Samnites in the Samnite Wars

Edit: http://cdn1.vox-cdn.com/assets/4821916/Roman_Republic_Empire_map.gif here is a nice gif which maps the rise and fall of the Roman Empire from 510BC - 530AD