The show revolves around the adventures of Peter Griffin, a bumbling but well-intentioned blue-collar worker. Peter is an Irish American Catholic with a thick Rhode Island / Eastern Massachusetts accent. His wife Lois is generally a stay-at-home mother and piano teacher, and has a distinct New York accent from being a member of the Pewterschmidt family of wealthy socialites. Peter and Lois have three children: teenage daughter Meg, who is frequently the butt of jokes for her homeliness and lack of popularity; teenage son Chris, who is overweight, unintelligent and, in many respects, a younger version of his father; and infant son Stewie, a diabolical child with adult mannerisms who speaks fluently with an upper-class English accent and stereotypical arch-villain phrases. Living with the family is Brian, the family dog, who is highly anthropomorphized, walks on two legs, drinks Martinis, and engages in human conversation, though he is still considered a pet in many respects.

There are many recurring characters on the show who appear alongside the Griffin family on a regular basis. These include the family's colorful neighbors: sex-crazed airline-pilot bachelor Glenn Quagmire; mild-mannered deli owner Cleveland Brown and his wife (ex-wife as of the fourth-season episode "The Cleveland–Loretta Quagmire") Loretta Brown with their hyperactive son, Cleveland Jr.; paraplegic police officer Joe Swanson and his perpetually pregnant wife Bonnie; and creepy old gay pedophile Herbert. TV news anchors Tom Tucker and Diane Simmons also make regular appearances (along with Asian Reporter Tricia Takanawa and Blaccu-Weather meteorologist Ollie Williams), as well as mentally disturbed celebrity Mayor Adam West (voiced by and named after the real Adam West).

Family Guy has not used an especially large cast of recurring minor characters (though this has changed to an extent in Season 4, with many one-shot characters from prior episodes reappearing in new episodes), and most of the episode plotlines center on the exploits of the Griffin family.