'The Stare' is an ability posessed by certian creatures in the Equestrian Wasteland. Looking directly into the eyes of creature with this ability is known to cause mental and physical paralysis. Littlepip encounters a few Tainted creatures she dubbed "Hospital Horrors" which possessed this ability. They were encountered in a hospital in Old Olneigh.
Fluttershy has a similar ability of the same name, notably used prior to the war. Her ability could force creatures (and in theory other ponies) into submission, and could allow her to overpower a cockatrice's own petrification stare.
- In the non-canonical side story Fallout: Equestria - New Roam, a type of creature known as chimeras are able to use this ability.