pets:

dogs - The most beloved pet of Rome, the dog was almost always named, and was often buried in a place of honor.
cats- Cats were imported from Egypt and trained to do tricks. However, they were primarily kept because of their abilities to kill mice and other vermin. They were rarely named.
ichneumons- A type of mongoose.
birds- Parrots, peacocks, pheasants, poultry, ducks, partridges, geese, and doves were all common pets.
monkeys- Primarily Barbary apes, monkeys were kept for their comedic nature and ability to entertain.
reptiles- Snakes (non-poisonous) were the most commonly kept reptile. Lizards were also kept.
deer, gazelles, fish- These pets were kept for their calming effect on the owner. The peaceful nature of their actions made them popular.
lions- Usually (but not always) domesticated.
tigers- Usually (but not always) domesticated.