The Romans were an advanced Human society on Earth, with a highly developed culture, that controlled the Roman Empire from around 500 BC to 500 AD. The Romans, and their Empire were centralized in Rome located in the future nation-state called Italy (later the capital was moved to Constantinople). The official language of the Romans was known as Latin.
The Romans were eventually defeated by barbarians, supposedly the ancestors of the German people. This was observed by a Nazi character in a holoprogram set in 1944 France to have been the result of the moral decay of the Romans and the superiority of the Germans. (VOY: "The Killing Game, Part II")
Spock's analysis of the degradation of the cultural development of the civilization found on Sigma Draconis VI, was comparable to the Romans' wars and eventual defeat by the barbarians. (TOS: "Spock's Brain"; VOY: "11:59")
Several scenes of Roman life, including the statue of Rome's founders, Romulus and Remus, being suckled by the Capitoline Wolf and a chariot race, were seen in the time stream as the timeline realigned itself after Jonathan Archer restored a damaged timeline. (ENT: "Storm Front, Part II")
The proverb, "When in Rome... do as the Romans do", often refers to the practice of following suit with what others are doing, particularly by observing and mimicking the customs of citizens of a foreign land the person is visiting. (DS9: "Let He Who Is Without Sin..."; ENT: "Babel One")
In 2268, the crew of the USS Enterprise discovered the planet 892-IV to be inhabited with Romans, mirroring those of Earth. This was evidence of Hodgkin's Law of Parallel Planetary Development. (TOS: "Bread and Circuses")