The New Yorker kindly gave a guide to understanding it's famously inscrutable cartoons this week.
I am a big fan of the cartoons that the magazine selects. Some are dry, some silly, some just fatuous. I get them, though. Of course there are plenty that resemble the "laughing squares" that Family Guy talks about, but Family Guy is an amalgamation of many cartoon styles and rips, including the New Yorker.
Taking the piss out of the New Yorker is easy, but before it, cartoons looked like this:

(Cartoon courtesy of lordprice.co.uk)
Nobody understands cartoons like these now, unless you happen to be a cultural historian of the Victorians. Then you might find them funny. The New Yorker changed cartoons into something quite different, less laboured in both ink and text.
New Yorker cartoonists like Saul Steinberg and Charles Addams created modern cartooning. In the pages of the New Yorker, they introduced surrealism into cartooning, the ability to have anything on the page, be it talking animals or postmodern rocks, and established the eternal themes for cartoonists, men on desert islands, Death calling at your suburban home (Family Guy rips this joke pretty consistently), the bloodsport of manners over dinner tables, the boss behind his boardroom desk, aliens landing, and most telling of all in New York, the psychiatrist's couch.
New York saw the birth of the lifestyle psychiatrist, the one that attends the dissatisfied and the angst ridden. Since this pretty much describes the lot of your average cartoonist, the psychiatrist's couch is an eternal theme because anyone, anything, can be there and be said. A universal theme for cartoonists, but one best done by Americans. They have a better ear for neurosis than the British, we're just whingers.
So we'd be lost without the New Yorker. No Family Guy without the New Yorker. Okay, maybe not. But Family Guy really is a series of small cartoons stuffed into a show. Three lines of blah, then someone gets hit in the face by a rake or there's screaming. In between they hit onto show tunes sung with gusto. There's no plot and you don't get it, but you can't take your eyes off it. You don't need to even watch a whole episode. You can just pick it up anywhere. In a word, I don't get Family Guy as a whole, but I keep watching to see if I will.
However, if you want to see if you get a cartoonist's mindset, you may take a quiz, pinning the right cartoon to the right answer.
Try the New Yorker's QUIZ to understand their cartoons here. I got 4 out of 5.









