Literally Fearless

Bravery is not the absence of fear, this trope is the absence of fear. As fear is part of a functioning human being, this is often considered a disability as much as a superpower, especially when the person so-afflicted defaults to an Attack! Attack! Attack! reaction in any threatening situation, despite the level of the opposition.

A Fearless Fool may not feel fear at appropriate times, but isn't necessarily totally devoid of the feeling. An Emotionless Girl lacks more emotions than just fear. Compare What Is This Thing You Call Love?, where a robot or alien doesn't have (or at least, doesn't understand) a different emotion.

Comic Books

 * One story line in the late-1980s Action Comics Weekly revealed that Green Lantern was literally a Man Without Fear: the power ring had removed Hal Jordan's ability to feel fear altogether the day that he first became Green Lantern. This was quite thoroughly deconstructed during the story, and by the time the story was completed, Hal was once again able to feel a normal amount of fear.

Fan Works

 * Hanna "Action Girl" Heller, from The Secret Return of Alex Mack and the greater Teraverse in which it is set, is a genetically-engineered Super Soldier who is simply incapable of experiencing (or understanding) fear by deliberate design. She does, however, eventually learn caution and how to rationally evaluate enemies vis-à-vis her own abilities, and her inability to feel fear comes in handy as a defense against at least one psychic attack made upon her.

Literature

 * Ashok Vadal of the Saga of the Forgotten Warrior series is renowned for his lack of fear in the face of demons, wizards, and lawbreakers he faces as the greatest among Lok's Protectors of the Law. It turns out Ashok is regularly shown to be emotionally stunted as a result.

Tabletop Games

 * "Immunity" to fear is traditionally a class feature of the Paladin in Dungeons & Dragons. Ravenloft makes it explicit that the Paladin isn't merely in control of his fear, but totally shielded from it. Accordingly it alters the class within the setting to only have protection from supernatural fear effects (meaning a paladin is still subject to intimidation, atmosphere, etc.) since one of the victims not having fear is a Story-Breaker Power for a horror setting.

Video Games

 * One line of dialog in Deus Ex allows the player character to insinuate that UNATCO's Cyborg troops have wiring to reroute their fear. If this is actually anything more than a snarky comment at a superior's expense is unclear: While they will retreat if heavily injured, their dialog for doing so suggests a tactical retreat rather than the fear most characters express, and other dialog confirms they are indeed unable to feel pain suggesting there is some metal rewiring going on.