Before the rise of Christianity, Rome was mainly polytheistic, meaning they worshipped a large pantheon of gods. There were specific gods that were worshipped more prominently in certain times or places throughout Roman history, but no god was worshipped at the exclusion of all others. Mars, the god of war, had special significance to the Romans and was often referred to as the patron god of Rome, though it's not clear if that tradition dates back to Rome's founding or was established later.
Interestingly, starting with the rise of the Roman Empire, Roman emperors began to be granted the title of divus and elevated to the status of a minor god. Augustus and many emperors who came after him were granted this title by the Senate upon their deaths. This designation did not replace the existing Roman pantheon or even place the Emperor above the other gods.
It's important to note that the Roman empire encompassed many different people groups with their own gods and beliefs. For example the Jewish people were under the control of Rome for a time. I'm talking about the core beliefs of the central Roman state, but religious beliefs varied widely across the empire.