Getting back to Family Guy...
Even when the general quality level was higher, it still had a couple of major problems. One of which is a main character who is absolutely odious and never, ever remotely funny. The "joke" of the character is that he's a complete idiot and therefore can get away with saying/doing anything, but you often get the sense that it's how the writers really think. A lot of the stuff he spouts is pretty hateful, but he never gets his comeuppance, just frequently winds up banging Lois. Furthermore... compare that with the idiot/arsehole foils of The Simpsons and South Park (Homer and Cartman): both of them have innate charm that makes them watchable in spite of anything. Not that Homer is frequently portrayed with a nasty or controversial side, but an alcoholic loser with an enabling, inexplicably trophy wife isn't inherently likeable. Cough, Family Guy. Cough indeed.
Another thing I frequently hated about it was all the female characters being judged from a sexualised point of view. Meg is ugly, therefore everyone hates her and she's considered worthless; all her storylines revolve around this. Lois is a hot nympho, she gets to be the babyface. Never mind that being married to Peter must make her absolutely f**king insane.
Still... like Predator Queen mentioned, regardless of the overall tone of the show, Family Guy has produced some fantastic jokes over the years. For some reason thinking of the "cool whip" sequence always cracks me up. Generally speaking, the less focus there is on Peter, the better the show is. It's hard to go wrong with Stewie, he has a bit of a Cartman factor.
On the subject of which, in my opinion South Park's general quality level has been slipping for around six years now. I think they got seriously burned out making Team America, and since then there's been a frequency of poor episodes that they very rarely had before. The constant stream of madcap randomness that made the show such a hit in the first place is long gone, and nowadays even in the better episodes it feels like every joke takes a long time coming, without sufficient payoff to make the wait feel worthwhile. There's enough quality to keep me watching, but I used to be f**king obsessed with this show.
Stepping away from the animated stuff, even Big Bang Theory isn't as good as it used to be. Relying on the same selection of seasoned comedy writers for each episode certainly ensures a constant rate of easy laughs, but their writing isn't as smart, and the characters aren't as sweet. It also feels more than a little like Two And A Half Men. But, again, still funny enough to keep me watching...
The one ongoing comedy show I'm aware of (and I'm sure there are plenty I'm not...) that's maintained high quality is The IT Crowd. LOVE that show, and it's bloody rare to see a show hinging on farce these days. I just wish they made it more often.
If I didn't say "in my opinion" before anything, pretend I did...