What achievements is Rome known for?
The city of Rome in the ancient world was called the eternal city, because it lasted for so long. In light of this, the achievements of Rome are vast and variegated depending on time period. In light of this, let me list a few achievements.
If you asked an ancient Roman in the days of Cicero about Rome's greatest achievement, he would say that the greatest achievement of Rome was in its ability to rule. For example, Cicero concedes that others are better at things like poetry, philosophy, and entertainment. But when it comes to statecraft no one does it better than the Romans. When we look at the historical data, we have to agree. Rome ruled a vast territory and they were able to do so, because of their political and managerial skills.
If we asked a early Christian in sixth and seventh centuries about the achievements of Rome, he would say that one of the greatest achievements of Rome was the leadership of Rome within Christendom. This bears some truth too, because Rome became place of the Pope and played a vital role in the growth of Christianity.
If we take a broader approach, we can mention many other achievements such as: Roman engineering (we still use Roman roads), construction of aqueducts (the longest one was 250 km), a Roman military ability. The list can go on, but these points should get you started.
Rome can be credited with many achievements. One of its most enduring legacies is its government under the republic. The Roman government was characterized by divided powers, with consuls, the Senate, and other officials sharing the reins of government. This government was closely studied by Renaissance and Enlightenment scholars, as well as the American revolutionary generation.
Another quite tangible legacy was the spread of Christianity. After its legalization early in the fourth century CE, Christianity quickly became the dominant religion--and later the official religion--of the Empire. It spread through trade, military conquest, and other means, and Rome (and later Byzantine, for Eastern Christians) became its administrative center. Other significant achievements were related to construction. Roman engineers and legions constructed walls, aqueducts, temples, government complexes, and especially roads throughout the Empire. Many aqueducts and roads were in use centuries later.
Roman law was another major contribution. It became the foundation of law codes throughout Europe, especially in France and Britain, where its legacy can be seen in the profusion of Latin terms describing legal concepts.