I've loved some of the topics here about how the Greeks and Romans practiced their beliefs, but one thing I'm curious about is how the treated the gods of other pantheons. I've always understood that the Romans were very cosmopolitan in their religion, and that even if they didn't worship these other gods, they still accepted their existence. Was this just for PR purposes or did they really actually believe that other gods existed outside of their borders?
Tacitus, when comparing the religious traditions of Rome and Germania, used the term interpretatio romana ("the Roman interpretation"; "Roman terms"). This term is still in use today by historians to describe the practice of Romans referring to foreign deities by their Roman equivalents. The Greeks did this too (interpretatio graeca).
In the original citation, Tacitus is describing a ceremony of the Naharvali, a Germanic tribe:
Among the Naharvali is shown a grove, the seat of a prehistoric ritual. A priest presides in female dress, but the gods commemorated there are, in interpretatio romana, Castor and Pollux. That, at least, is the power manifested by the godhead, whose name is Alci. There are no images, no trace of any foreign superstition, but nevertheless, they worship these gods as brothers and young men.
So, when describing foreign gods and goddesses, they put them in their own religious terms.
There is also, incidentally, an interpretatio germanica,* a process by which the Germanic tribes made correspondences between their gods and Roman ones. This is still present in the days of the week in English: when the Romans (late in the empire) started using terms like Iovis dies (cf. French jeudi, Spanish jueves, etc) the Germanic peoples associated Jupiter with Thor, giving us the term Thursday.