The Geass in Lelouch's (Code Geass) eyes grants him the power of "absolute obedience," allowing him to hypnotize others and plant post-hypnotic suggestions in their minds.
Though initially limited to one, Lelouch's (Code Geass) Geass eventually evolved to encompass both eyes.
Hades (Fairy Tail) possesses the Demon's Eye. Along with increase his already incredible Magic Power, the eye allows him to perform one of Zeref's Black Arts and use Living Magic.
The Uchiha clan's Sharingan (Naruto) grants superhuman eyesight, the ability to read body language, hypnosis, and the power to copy the jutsus of other ninja.
The Mangekyō Sharingan (Naruto) is an advanced form of the Sharingan that has only been activated by a handful of Uchiha. Along with possessing standard Sharingan abilites, the Mangekyō Sharingan grants the ability to access Amaterasu's flames and perform Susanoo.