Davis, one of the best damn artists MAD Magazine ever had (often partnering with writer Dick DeBartolo to create the best damn film & television parodies MAD Magazine ever ran) did a lot of advertising work. He created the cockroaches that screamed "RAID?!?!?!" before being obliterated, for example. And he also turned out movie posters galore, seeing as how he was a damn fine caricaturist and all.
A typical madcap movie poster would feature the stars prominently in the center while hordes of crazies ran about behind them, often doing stuff you'd get to see in the film if only you weren't a cheap schmuck who won't cough up enough for a ticket! (Hmm. Seem to have channelled certain MAD editors for a moment. So there! Fa!) And boy, were there a lot of crazies involved. So many crazies! Often the crazies got to hold signs, though I'm not sure if that was more of a sign of the late 60s protest culture as it was an overall stylistic decision. (It does help when you don't have word balloons to work with, I guess.)
Other MAD artists got in on this craze, too, such as Jack Rickard. Rickard holds the dubious honor of doing the poster for Up The Academy. I'd say this was MAD Magazine's first and only foray into feature filmmaking, only it was so bad they disowned it and paid Warner Bros. to take their name off the damn thing. Just as it is with the non-film Highlander 2, "Mad Magazine Presents Up The Academy" doesn't exist.
Bad films were par for the course, unfortunately. With a few rare exceptions (such as It's A Mad, Mad, Mad, Mad World, The Bad News Bears and Woody Allen's Bananas) the films that chose to use these kinds of posters in their promotional campaigns weren't very good. We're talking stuff like Peter Lawford and Sammy Davis Jr's flops Salt & Pepper and One More Time. If you saw a poster like that out, you may have a stinkburger on your hands -- or at least one that just never stood the test of time. (Your decision to be a cheap schmuck then wasn't all that bad. But don't let it get to your head!) I love the poster art, but most of the films I could live without.
The most famous of these madcap posters, the one for Animal House, was not drawn by Jack Davis or any of the Usual Gang of Idiots. It was done by artist and frequent National Lampoon contributor Rick Meyerowitz. Now you know. I hope you can win a bar bet with that knowledge someday.
Internet addendum: See? Some stuff you just can't do on Twitter. I tried it. Didn't work, and Twitter ate 1/3 of my three-message opus. Well!