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In Family Guy, I saw around 2 or 3 episodes showing us a rodent falling off Quagmire's. What does it represent?
As @Longshanks commented, it is a joke at the expense of the story about Richard Gere stuffing a Gerbil up his rectum (which Snopes tags as fake).
In Family Guy, the gerbil is called Tony and it's just another way to show Quagmire's extreme promiscuity and sexual deviancy.