What type of joint allows rotation and is often compared to a ball-and-socket joint?

The pivot joint is specifically designed to allow for rotational movement around a single axis. A key characteristic of a pivot joint is that it enables one bone to rotate around another, exemplified by the joint at the base of the skull (atlantoaxial joint) which allows the head to turn from side to side. This type of joint is often compared to a ball-and-socket joint because while both allow for movement, the ball-and-socket joint permits a wider range of motion, including rotation, but is not limited to it.

In the context of the provided choices, hinge joints primarily allow movement in one direction, like bending and straightening, without rotation. Cartilaginous joints provide limited movement and are typically meant for stability rather than rotation. Synovial joints encompass a variety of joint types, including ball-and-socket and hinge joints, but do not specifically denote the capacity for rotation as pivot joints do. Therefore, the pivot joint is the most fitting answer given its unique ability to facilitate rotational movement.