The Romans were extravagant in many things, religion among them. In their pantheon of hundreds of deities, the Romans revered twelve above all, and these are patterned after the Olympians of ancient Greece. The chart to your right shows the major gods and goddesses as well as their Greek and Roman equivalents. 

The Romans thought of them in male-female pairings, either married (as in the case of Jupiter and Juno) or just casual (Hermes and Venus). The twelve appear as Dii Cosentes, a kind of divine council that watched over the Roman Forum. Of the twelve, the Romans did not include Hades (Pluto); as Lord of the Underworld, he did not dwell in Olympus. And some deities differ depending on the source (Vesta does not always make the cut).

Of course, the Romans gave their adopted Greek deities Latin names. Some of the Roman and Greek gods and goddesses—Apollo, for instance—answer to the same name in both languages (from https://ancienthistory.about.com/)

The Romans were always trying to keep on the good side of their gods. They made offerings at temples and shrines to make them happy. They also borrowed new gods from the people they conquered, like the goddess Isis from Egypt and Mithras from Iran.

Some emperors were declared gods too, usually after they died. They hoped this would make emperors even more powerful and respected.

Later on the Romans became Christians. Christianity was made the official religion of the Roman Empire by the Emperor Constantine in the 4th century AD. Before then, Christians got into trouble because they refused to worship the emperor as a god. Some Christians were arrested and put to death (from BBC Bitesize History - What did the Romans believe?)

Look at the image below to get an idea of the family tree of the gods and goddesses of ancient Greece and Rome.