The Romans respected the vermin-catching abilities of the domestic cat, but also saw them as exotic pets and sacred animals. They associated the cat with liberty and divinity and so the cat was the only animal allowed to walk freely around their temples. Libertas (the goddess of liberty) was often depicted with a cat at her feet
They also associated cats with the Roman Goddess Diana, the Queen of the Hunt. One story tells of how Diana escaped Typhon (an evil dragon-like creature often associated with the Egyptian God of Storms, Set) by transforming herself into a cat - although in other versions of the story she is transformed into a dog!
Diana was often associated with the Egyptian Goddess Bast, a feline goddess who was (amongst other things) a guardian of the home and family and like the Egyptians, the Romans considered that their cats represented the warmth and safety of home. Sacrifices were made to their cats during both funeral and wedding celebrations to get the cat to bless the participants. Cats often acted as mascots and travelling companions for Roman armies whose grain stores the cats would protect.
The modern city of Rome is still a haven for cats. An estimated 300,000 feral cats inhabit the monuments of the city and were given the protection in 2001 of confirmed as part of Rome's "bio-heritage". There is a cat sanctuary around the Torre Argentina (where most of the temples of Roma are situated and the location of the murder of Julius Caesar) and the cats are fed and protected by many of the women of the city - known as "gattara" ("cat women). So the cats still have free access to the ancient temples!