At its peak, Family Guy was an excellent source of humor, with numerous types of jokes. Consider two favorite scenes of mine from "The King is Dead":
Lois gets a call from someone asking if she would take over as play director. While she thinks it over, everyone in the room stares at her, anticipating her response. Then they cut to Tom & Diane on the news, ALSO watching to see her response. As soon as she says she'll do it, Tom says "This just in: Lois Griffin is named the new artistic director of the Quahog Players." And if that wasn't enough, a picture of Lois on the phone appears next to Tom, like they had cameras in her house and captured her reaction shot.
Consider another scene, this time in a cutaway, where we see Einstein working at a patent office. A man named Smith comes up and says he has what he calls "Smith's Theory of Relativity". Einstein knocks him out and steals his work. Now that joke would be funny on its own, but then he does the same thing to GOD in a later cutaway.
A lot of the humor is also derived from top notch comic timing, like in "Death Lives" when Peter is casually saying to Death how he'll get him cleaned up for his date. In mid-sentence he takes off Death's hood to reveal a hideous skull, to which Peter screams in horror. A couple seconds later he puts the hood back on and casually continues his interrupted sentence like nothing happened.
Like others have said, some of the humor also derives from the unexpected. Consider a cutaway in "Dammit Janet" when Peter is in the Outback and pokes a crocodile multiple times. The obvious outcome of that joke would be for the fed-up croc to snap at Peter. But it doesn't move. And out of nowhere, a koala flies at Peter's head.
Or in "Fifteen Minutes of Shame" when Peter says "HERE'S what I think of your contract!" The cliched thing to do would be for him to tear it up. But instead he simply hands it back to the exec and says "I think it's awful."
Then there are jokes about how stupid Peter is, but nevertheless provide some humor. Like in "Brian in Love" when, by simply hearing Lois say the word "bond", he says "Bond? JAMES Bond!" Or in "One if By Clam, Two if By Sea" when Peter is so clueless that he doesn't realize the person getting arrested on TV is him.
I could go on and on, but hopefully this gives an idea of why -I- like it, anyway.