I've heard claims that it's bad to stretch the neck by tilting it all the way back, or by doing neck circles. Here is one such article
Research is showing a connection between extreme neck positions-the head bent way back for the beauty salon shampoo, prolonged dental work, painting ceilings-and possible stroke caused by less blood flow from the vertebral arteries. Elderly people and those predisposed to heart problems should be especially cautious because of possible clogged arteries.
Also, rolling the head back during a neck circle puts maximum compression on the spine.
"It sort of grates and grinds the vertebrae," said Linda Tremain, a physical therapist and athletic trainer for the Caremark practice in Willowbrook. "It is an unnecessarily stressful exercise."
As to being safe, I've personally gone to a few fitness classes that did the stretch and I asked a massage therapist who said "you have to reef on your neck pretty hard to make it go back far enough to do damage" (however, I wouldn't consider a massage therapist an authoritative source on the matter).
Is there any evidence that shows that tilting your head back for as far as it can go (without the use of any additional force, for example by your hands) for a short amount of time (e.g. a minute or less) is unhealthy or harmful?