Most today think of Roman religion in terms of its pantheon of gods and goddesses, such as Jupiter, Venus, and Mars (or their Greek counterparts Zeus, Aphrodite, and Ares). Certainly, this pantheon was central to civic life. Touring an ancient city, one would see dozens of temples (some of immense size) dedicated to such deities. These gods were thought to act as benefactors both to the individual and to the city. Yet, should one neglect these deities, they could become angry and injure the individual or society. Thus, the charge of "atheism" against early Christians (who refused to worship such gods) was effectively a concern that rejection of civic gods could lead to widespread catastrophe. Ancient pagan worship assumed a kind of ritual contract where, if specific words were said, and if certain sacrifices or libations were performed, the god/goddess was obligated to respond to benefit the worshiper.
Nevertheless, beyond the great gods of the pantheon, each household also worshiped some of the hundreds of other lesser deities that were thought to rule every aspect of human life. Thus Roman houses typically had at their entrance a shrine, a lararium, where daily libations were poured to these household gods.
Hero worship in antiquity could lead to the elevation of great conquerors as gods. Thus some revered Alexander the Great as a god in his lifetime. Perhaps it was this tendency that allowed the emperor, as patron of the whole empire, to be received as a god, especially in Asia Minor where extravagant temples to the emperors were built even before the NT period. Some emperors (esp. Gaius Caligula, Nero, and Domitian) were known to encourage their own worship.
By the first century A.D. mystery religions had become widespread throughout the empire, conducting secret ceremonies to gods and goddesses of Asian or Egyptian origin. The inductees learned the mysteries and participated in secretive worship practices.