Principessa is Quagmire's purebred Persian cat. When he leaves her with Lois while he goes with Joe and Peter to try to hunt down Bobby Briggs who shot and paralyzed Joe in "Joe's Revenge", he leaves very exacting instructions with Lois on her care. Brian becomes jealous of the attention the cat gets and gives to the family, but tries to imitate it in order to get to feel Lois' breasts when it kneads her while she is asleep.
Principessa appears in the special opening of "Total Recall" being held by Quagmire.
After winning big in Las Vegas, Brian takes out a hit on Principessa in "Roads to Vegas", although the DVD commentary for "Quagmire's Quagmire" notes that her fate is not necessarily resolved.