Farthest head rotation by an animal

Owls (order Strigiformes) can rotate their head the farthest of any animal, able to twist their heads through 540 degrees in full rotation, or 270 degrees in half rotation to the left and right, if starting facing forward. This incredible ability is useful because although their vision is acute, particularly at night, they do not have the ability to move their eyes (i.e., they can only look straight ahead). The flexibility is enabled by 14 cervical (neck) vertebrae, compared to seven in humans, and also adaptations to the vertebrae and the size/structure of the carotid artery, which allows for the extreme rotation without blood supply to the brain being cut off.

It's worth noting that while owls might be capable of turning their heads by 270°, they will generally stop at 180° (stopping when the beak is in line with the spine), then turn their head the other way.

In the mammal kingdom, the unique spinal morphology of tarsiers means they are capable of turning their heads nearly 180° in each direction.