They absolutely did. First off, let's define our actors. Starting at, let's say 200 BC, the Greek states as we'd imagine them today were in three major parts: Macedon, the Aetolian League and the Achaean League. During the Second Punic War (Rome's famous conflict with Carthage, a naval state centered in modern day Libya), Macedon allied with Carthage and was fought briefly and to a stalemate by a beleaguered Rome.

After Carthage was broken in the conclusion of the Second Punic War, expansion into Greece was at the top of the Roman agenda. There would be four 'Macedonian Wars' in total, including the brief one during the Second Punic War, with Rome over the course of half a century expanding onto the peninsula and into the Balkans. Rome won each war, declaring itself initially the 'protector of Free Greece', this ruse was seen through by furious Greek partisans, who led the city states to ally in part against the expanding Roman state.

But the momentum of Rome (and the technologically superior tactical formation known as the maniple) could not be stopped. In the Macedonian Wars' conclusion, all of Greece was reduced to the Roman provinces of Macedonia, Achaea and Epirus, ending Greek independence for centuries (or millennia, depending on your perspective on the Byzantines) to come.

Rome butted heads with Magna Graecia (latin for "Great Greece"). who were Greek Colonists who settled in southern Italy. early in Rome's republic. The beleaguered Greeks called upon Pyrrhus of Epirus to come to their aid, but Pyrrhus fought some indecisive battles against the Romans and didn't manage to the round up the support neccessary to mount a sustained campaign against the Romans before having to return. He was likely to try again until he was killed in one of his Greek campaigns. And Magna Graecia eventually fell to the Romans.