I did not have such assignments in my AP courses (U.S. govt. and American history).
I got a 4 and a 5 on the exam, respectively.
Summer homework is NOT necessary. I simply will not subject my students to it.
For AP US History, we had to read one book on an historical figure and then write a pseudo-report that we'd present to the class in the first week of class. Kind of a pointless assignment, if you ask me.
Then in AP English we had to read some Americana lit (2 books, I think) and write an essay on them. It sucked and nobody really did it.
However, in AP Calculus, we were given a batch of problem sets covering a lot of algebra/trig that we were required to turn in at certain points throughout the summer. That way when we started the class, we weren't rusty on some very perishable information, and I thought it was a good idea.