South Park is just a given. Construction paper look and choppy movements; the lower quality look automatically makes it funnier. The bug eyes and smiles you typically see on the characters give the impression of a cutesy cartoon, but it ends up being quite the opposite. This was a show I first found out about around first grade and the mixture of animation and swearing and inappropriate themes had me sneaking some peeks whenever my parents weren't around to find out what I was watching.
Another choppily animated show, The Life and Times of Tim. The lack of animated expressions mixed with the dryness of the humor really make it a riot. Season 2 has really improved in the background department, but the staff of the show said they have had to hold themselves back in what they can do artistically in order to retain the amateur animation style.