What are places which Ancient Rome had conquered?

Ancient Rome did actually take over any countries. Counties in the modern sense of the nation-state did not exist in antiquity. There were thee types of state formations: kingdoms, independent city-states and territories of ethnic groups which were named after the group in question (e.g. Etruria, land of the Etruscans, Latium, land of the Latins). Most ethnic territories were not centralised and were collections of either independent city-states or impediment tribes. Sometimes, all or some of the tribes of an ethnic group formed alliances (leagues or federation) for military purposes. They were not political amalgamations. The Latin Words natio (plural nationes) did not refer to nations. It referred to ethnic groups.

In terms of modern day countries, the Roman Empire covered the following modern day countries or parts of modern countries:

Western Europe: Italy, Malta, Spain, Portugal, France, Belgium, Luxembourg, Holland south of the river Rhine, southern Germany and part of central Germany, Switzerland, Liechtenstein, Austria and England and Wales.

Eastern Europe: western Hungary, part of western Slovakia, Slovenia, Serbia, Croatia, Bosnia and Herzegovina, Montenegro, Macedonia, Albania, Greece, Bulgaria, part of Romania, Moldova and a slither of western Ukraine.

Asia: Turkey, Cyprus, Armenia, northern Iraq, Syria, Lebanon, Israel and Palestine, Jordan, and the northern part of the coast of the Red Sea in Saudi Arabia.

Africa: Egypt, the coastal part of Libya, Tunisia, the coastal part of Algeria, and northern Morocco.