Literally Fearless

There is only one man in Lok who does not know fear. Of course you're afraid. Fear is the tool that keeps most alive

—Ashok Vadal, House of Assassins

Bravery is not the absence of fear, this trope is the absence of fear. As fear is part of a functioning human being, being Literally Fearless 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, monster or alien doesn't have (or at least, doesn't understand) a different emotion.

A lack of fear can lead to Bullying a Dragon or Suicidal Overconfidence‎.

Examples of Literally Fearless include:

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 removed Hal Jordan's ability to feel fear the day he became Green Lantern. This was thoroughly deconstructed during the story. 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 incapable of experiencing (or understanding) fear by deliberate design. She eventually learns 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.

Film

The titular Terminators in the Terminator franchise, for the obvious reason that they lack organic brains. They only retreat if they feel they can't fulfill their tasks, but otherwise will jump headfirst even if it means their destruction is imminent.

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 Vadal" was magically programmed over a slave boy's real identity to spare the Vadal family embarrassment after he winds up accidentally bound to Vadal's Ancestor Blade, and his sense of fear was removed so he was more likely to die and make room for a real Vadal to bind to the blade. It didn't work, instead creating the Law's most fearsome enforcer who slaughters the heads of the clan for breaking the Law when he learns of their acts. Ashok is regularly shown to be emotionally stunted as a result.
"The Story of a Boy Who Went Forth to Learn Fear" is a Grimm's fairy tale that explores this trope, as the title character travels the world to learn what fear is, specifically the sensation of shudders. After marrying a princess, the princess's chambermaid helps him learn what "shuddering" is... by pouring jumping minnows all over him when he's sleeping. The man is so thrilled he finally understands.

Live-Action TV

As an artificial being, Star Trek: The Next Generation character Cmdr. Data has no capacity for any emotion, including fear, a fact that he laments.

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.

Theatre

The Ring of the Nibelung crosses this trope with Achievements in Ignorance when Siegfried succeeds in reforging Nothung for the very reason that he knows not fear. Literally. Never mind that Mime with all manner of skill in smithery can't do it, Siegfried can somehow do it just from having complete ignorance of the concept of fear.

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.
Fear is an actual status in the Persona series, which makes highly probable for those afflicted with it to ignore commands and, in case of everybody but the MC, outright flee from battle and not return. However, the skill Null Fear prevents the status of being inflicted on a party member at all. Most bosses are outright immune to it from the get-go.

Western Animation

One episode of Batman: The Animated Series, adapted from a post-Crisis comic, features Scarecrow unleashing a gas that removes fears and inhibitions from select victims. Batman gets dosed while investigating undercover, and loses the fears that normally hold him in check—including the fear of sticking to his code of Thou Shalt Not Kill. Tim Drake as Robin has to alternate keeping Batman from crossing the line and stopping Scarecrow to get the antidote.
In Trollhunters, after Draal befriends Jim, they talk about Jim's jitters regarding his playing Romeo aside his crush Claire, namely that Jim and Claire have to kiss onstage as Romeo and Juliet. While Draal thinks that kissing sounds weird, he gives Jim a Grit-Shaka, a troll amulet that removes fear. It becomes Gone Horribly Right as Jim without fear becomes a Large Ham and tries to kiss Claire before rehearsal; to make matters worse, he seeks out The Dragon Bular in the sewers to challenge him for a fight, breaking Rule One of being a Trollhunter. Bular has to remove the Grit-Shaka to get a clear shot on Jim, who has no memory of the previous day and runs for it.