Sonar Sight

A character has been blinded, probably at birth. Now he has a superpower that sort of acts like sight, but employs sound instead, much like a bat.

This comes in two varieties, passive and active. The passive variety uses ambient noise and its reflections to build up a "map" of the character's surroundings. Active is similar, but instead of relying on the environment to generate the necessary sound, the character produces his own, usually automatically and unconsciously, typically in the ultrasonic range. Active (usually) provides a "clearer", more detailed image, but shouts "here I am, right here!" to anything that can hear the pulses its user generates. Passive may be "fuzzier" and leave its user at the mercy of his environment (a sound-deadening room, for instance, will leave him almost blind, and too much sound can "flashblind" him), but is also far better suited for stealth.

Examples of Sonar Sight include:

Comic Books

Daredevil - his ability is generally portrayed as passive.

Film

The 2003 Daredevil film actually rendered a visual version of the effect in action several times, in quite a striking way.

Video Games

The game Beyond Eyes has a little girl who lost her sight. She can "see" using sound alone. It's used for solving different puzzles
Cassie Thornton, the star of Perception, is blind and "sees" with echolocation.
An upcoming^[when?] VR game, Blind, has the player step in the shoes of a little girl, who uses echolocation.
In The Elder Scrolls V: Skyrim the Falmer have been rendered blind by centuries of living underground. Their hearing is good enough to use a bow, but magically silencing your footsteps makes them unable to detect you if you don't otherwise make noise.
Muffled Warfare an early access indie fps, were all the player characters are blind and uses sounds to see, shoot, and silence their foes.

Western Animation

Toph Bei Fong from Avatar: The Last Airbender, born blind. She uses earthbending to "see" through the soles of her feet.

Real Life

This man uses bat-like echolocation to see.