Lois: It seems today / that all you see / is violence in movies and sex on TV!
Peter: But where are those good, old fashioned values...
Chris, Meg, Brian, and Stewie: ...On which we used to rely?
The whole family, joined by backup singers: Lucky there's a Family Guy! Lucky there's a man who / positively can do / all the things that make us...
Stewie: ...Laugh and cry!
The family: He's... a... Fam...ily... Guy!
Family Guy is an Animated Series created by Seth MacFarlane about a Dysfunctional Family who...well, that's about it, really. It presents us with four main characters--slow-witted blue-collar jerk Peter, who is basically a crueler, more imbecilic, and often more cheerful Al Bundy; smart and efficient (and constantly closer-to-Earth) Housewife Lois; insecure teenage Meg; and good-hearted but moronic son Chris--and puts them through a series of adventures usually sparked by Peter's selfishness and/or idiocy. In addition to these somewhat cookie-cutter characters are two additional ones, Brian the martini-sipping intellectual dog and Stewie the laser-toting megalomaniac baby, although they've gotten much more screen time in recent seasons.
Chaotic and somewhat out of the ordinary, the show is notorious for its Cutaway Gags, as well as targeting literally every subject under the sun with a million gags per minute. Depending on who you ask, it's either sloppy, unstructured and tasteless, or unorthodox and acceptably simple entertainment. With later seasons, the randomness increased and character dynamics shifted, with Stewie becoming less of a mad conqueror and more of a showman with homicidal, homosexual, and/or violent tendencies, Meg becoming a Butt Monkey (supposedly due to the fact that the writers felt her too bland a character) and Brian becoming more and more of a pompous loser. The animation style became stiffer, and the show as a whole became more mean-spirited. It's drawn flak for this, but its fanbase is as loyal as any other.
The show made history for American network television for being Uncanceled -- twice. FOX announced the show's cancellation after its second season in 2002. The show was resurrected not long after, but ratings suffered as its time slot changed constantly and it competed against the ratings-behemoths of Survivor and Friends. After the third season, FOX called the show "canceled for good". But in 2005, the show was resurrected yet again, due to popular request, impressive ratings for the reruns on Adult Swim, and unusually successful DVD-set sales. Family Guy is now one of the network's most successful franchises, promoted by the suits with the same fervor as Twenty Four, The Simpsons, and American Idol. This made Seth MacFarlane THE highest paid Hollywood writer for a few years after its second revamp- it allowed him to produce the Spin-Off series The Cleveland Show, and American Dad, both under the same studio, along with the Star Wars spoof Family Guy Presentslaugh It Up Fuzzball.
As a final point, it's worth remembering Seth MacFarlane is not as heavily involved in the writing of more recent episodes as you might think. While he's still an executive producer, and thus can veto scripts, chances are he's not the one you should aim bile at when it comes to specific gags, aesops and messages in the plotlines.
Has its own wiki