Aspirations are one thing, but actually seizing and holding the territory required a great expenditure of resources, and what Rome needed most was a large and ever-expanding army, which eventually had to be professionalized. Professionalization of the army led to even greater changes in the organization of the state, the most important of which was the destruction of the republican system of government. After a relatively short initial defensive period, Rome's army was turned toward expansion. Its final mission was to hold the long border and try to slow shrinkage of the empire. It was also necessary to tend to the army's constantly growing "tail", everything it took to keep it in the field. The vast expenditures in money and emotion associated with expansion initially stimulated Rome, but the cost of defending territorial gains could not be sustained indefinitely. The "Rise and Fall" scenario is familiar enough that it doesn't need further explication here.
The timeline and actual extent of Rome's territorial expansion (and later contraction) are easily found. Those lucky enough to live in Rome can see a series of large 20th Century maps on the outer wall of the Constantine/Maxentius basilica -- they are about halfway between the entrance to the Roman Forum and the Colosseum on Via dei Fori Imperiali.
Both the timeline and more detailed maps also are available on the Internet, and here is where to find them:
From the University of Calgary: http://www.ucalgary.ca/applied_history/tutor/firsteuro/roman.html
MacKay lecture on expansion: http://www.ualberta.ca/~csmackay/CLASS_365/Wars.To.Sack.html
Links to primary sources on Rome's expansion and contraction (as well as other aspects of Roman) history are available on the Rome page of the Internet Ancient History Sourcebook: http://www.fordham.edu/halsall/ancient/asbook09.html