1: Some of the characters are unoriginal and uninspired. The father, mother, teenage son and teenage daughter have no interesting attributes. They're just cardboard cutouts that seem to say "insert politically incorrect joke here, humor not necessary".
2: Some of the characters are not only unoriginal, they're ripoffs. The fucking baby is a ripoff of Brain from Animaniacs and Pinky and the Brain. That's not to say that the source of said ripoff is any good. Maggie Simpson is a much more believable example of an infant with great intellect. You don't have to pount it into the heads of viewers. The dog is a ripoff of "Buck" from "Married With Children". Far be it from me to sing the praises of the long-running white-trash Odyssy, but Buck was far more subtle in it's use of the whole cliche "animal is smarter than family" plot device.
3: The show utilizes the most basic comedic devices known to man. Great comedy twists established concepts to make a humorous situation. Turning an established concept completely around results in a slightly comedic situation. Example: on The Simpsons, Itchy and Scratchy Land is a *twist* on the run-of-the mill theme park. Now, let's get back to the *twist*. Unlike normal theme parks, the inspiration is two ultra-violent cartoon characters. Is it likely that such a thing would happen in the real world? No. Impossible? No. Here's an example of Family Guy humor for contrast: rather than take their children to Chuck E. Cheese, they take them to a torture-themed children's restaurant! Hold the phone, my sides are splitting with laughter! This utter ridiculousness has no place in professional comedy, whether it's live action or animation. Does that mean it might be funny on a playground between two eight-year-old kids? Maybe. Does that mean it should be on fucking prime-time television? No.
4: Simply bad jokes. I can get all intellectual on the subject of how Family Guy is a ripoff or how they go about comedy all wrong, but that's not necessary here. There is no explaination needed for bad comedy. A guy tells a woman she has "nice hooters". She turns around, she's holding two owls! Wake me up, I must be dreaming! I'm in comedy heaven! If you couldn't detect the sarcasm in that last sentence, you must be retarded, and thus, a card-carrying member of the target audience of "Family Guy"
5: Cashing in on the animation wave: It's a bad show. The characters would never fly in live-action. Animation and live-action are two different mediums. A good test to look beyond the allure of animation is to try to picture the characters in live-action. Look at the Simpsons, (you may question my repetition of citing the Simpsons as the high watermark for quality animation. I make no qualms about it, the Simpsons is the Bible of animation) a good portion of the show's main humor would be lost in the transition between animation and live-action, but the characters would still be engaging, interesting and identifiable. Would the characters in Family Guy make the same transition? No, because there are no characters in Family Guy. Sure, some animated properties simply could not be done justice in live action, but when you're talking a human family, that excuse is not valid. But we live in a time where 37 animated shows premiere every week. A show that would be laughed out of a television studio pitch meeting before the animation boom is hailed as "The next Simpsons!" Animation does not change the fact that comedy sucks.
I think the show sucks. The everyman thinks the show sucks, professional animators and animation writers think the show sucks (jokes at the show's expense have popped up on "The Simpsons" and "Clerks [The Cartoon]"). As with virtually every entertainment property, there is a small legion of fans that loyally stands by the show, but I'll go so far as to say that every single fan of "Family Guy" is an idiot who doesn't have the attention span to finish this post. You guys are simply the bottom-feeders of comedy fans.
"We'll go dancing, set fires, tag buildings, slash tires, ride go-carts like Shriners or just hang out at Fred Meyers." Glen Phillips, "Fred Meyers"