The Romans and the Greeks shared the same gods, though under different names. They had similar, though not identical outlooks on the world. They both believed that their cultures were superior to all other cultures, allowing them to refer to outsiders as Barbarians. They both developed a slave culture in which wealthy citizens bought and sold slaves for manual labor, for crafts and skills, and, sometimes as the educators of the young.

Similarities include the use of a lot of gods and goddesses, heroes, and mythical creatures. 
Gods/Goddesses: Zeus, Hera, Athena, etc.
Heroes: Achilles, Perseus, Hercules (the Romans borrowed him from the Greeks and Latinized his old name, Heracles, so it became Hercules)