The Romans were very fond of the Hellenic culture.

Some others might know more about the cultural aspect, but the religious aspect was of great importance and interest to the Roman society. The reason for this was the fear of bad things. To combat crop failure, military defeat, disease, etc. the Romans "imported" foreign religions. Two of the best examples of this are the import of Isis from Egypt(where the monolith was placed in Rome as a symbol of consummation) and Mithras from Babylon(I believe) which was treated as a mystery cult especially for the upper class.

Further, the distinction between cult and religion was blurred at times, but you can think of it as local and regional. They also used "ancient" rituals for auspices, like auspices(origin of the word). This was a way to take signs by the flight of the birds. My favourite is Haruspicy, an Etruscan practice, where the practitioners(haruspex) had to be Etruscan or of Etruscan descent.

These are just examples, but each era and region had different imports, and even the Jews were imported at one point. As with the Jews, some of the religions were banned.

Omens, Prophecies, and Oracles in Ancient Decisionmaking. In K. Ascani, V. Gabrielsen, K. Kvist, A.H. Rasmussen (eds.), Ancient History Matters (Studies Presented to Jens Erik Skydsgaard on His Seventieth Birthday), 173-184. Roma 2002.

What have the Romans ever done for us? How to Win Wars and also the Peace. In Tønnes Bekker-Nielsen (ed.), Rome and the Black Sea Region. Domination, Romanisation, Resistance (Black Sea Studies, 8). 133-151, Aarhus, 2006

Animals, Gods and Humans. Changing attitudes to animals in Greek, Roman and early Christian Ideas, London/New York: Routledge 2006

Globalization and Religion in the Roman Empire", i Luther H. Martin og Panayotis Pachis (red.), Hellenisation, Empire and Globalisation: Lessons from Antiquity, Thessaloniki: Vanias Publications, 2004, 85-99.