I don't know if this is the genre you are thinking of, but one of my favorite easy party games is called "picture telephone."

Everyone starts out with a sheet of paper and pen or pencil. Then at the top of the paper, they write a sentence or description, like "divers discover buried treasure" or "badgers having a tea party." It could be anything really. Then everyone passes their paper to the right. Next, underneath the description on the paper they got, everyone tries to illustrate the sentence or description. When they are done drawing, they fold down the paper to cover the description they drew from and pass the paper again. The NEXT person has to write a new description for the illustration they see. You keep folding down and passing, alternating between drawings and descriptions, until you run out of paper. Then you unfold and read them and enjoy the hilarity.

Alpaca,

We played your drawing game - it was hilarious, thank you

Ooooh I am so glad you liked it! We used to play it in the co-op where I lived and we would laugh about it for hours.

Well, I don't know about content per se, but I think there is a delicate balance to what you pick for a starting sentence in terms of how hard it is to draw.

If it's too hard to draw or too complicated, the next person might just give up in frustration, or too much will get lost.

If it's too easy, you won't get enough change throughout the iterations, so it won't really be funny.