The ability to be aware that one's Universe is fictional, and potentially use this to act in otherwise impossible ways within their fictional universe.
Fourth Wall Breaking
User is aware that one's Universe is a fictional/false one, allowing them to carry out acts that, within the Universe, would otherwise be impossible. Depending on the extent of the user's power, one could potentially gain the powers of Reality Warping and/or Omniscience within the context of their own false Universe.
Rosencrantz (Rosencrantz and Guildenstern are Dead)
Guildenstern (Rosencrantz and Guildenstern are Dead)
The Player King (Rosencrantz and Guildenstern are Dead)
Deadpool (Marvel) shows awareness that he is in an illustrated story.
Uatu the Watcher (Marvel)
Pinkie Pie (My Little Pony: Frendship is Magic) can view and shatter the fourth wall.
Ajimu (Medaka Box) is aware that she is in a manga and will be animated.
Neo (The Matrix) is aware that The Matrix is a false existence, and as such can manipulate its reality, stopping bullets in their paths.
The title character of the film Rango is aware of the fact that he's a fictional character in the film.
Many Kid Icarus: Uprising characters like Pit and Viridi, often break 4th wall by making video games references or mentioning that they're in a video game themselves
Sonic talking to the audience in the show's segment "Sonic Sez"
Lyssa Drak (DC)
Kirihime Nastuno - "The protagonist has enter the story." (Dog & Scissors)
Kuzco (The Emperor's New Groove)
Scott Pilgrim (Scott Pilgrim comics) frequently shows an awareness that he's in a fictional universe, telling many other characters to "read the book" when they ask questions regarding the events of previous chapters or volumes.
The Squid Sisters (Splatoon), Callie (left) and Marie (right), are aware that they are in a video game and occasionally reference that fact.
The Twelfth Doctor tells the viewers to Google the bootstrap paradox (Doctor Who)
Neptune (Hyperdimension Neptunia) Breaks the fourth wall
Uncle Grandpa (Uncle Grandpa) is shown to be aware of the fact that he is in a cartoon, and would sometimes acknowledge the fictional world around him and the viewer.
Sardonyx (Steven Universe) is implied to have a limited awareness of the fictional nature of her show, making references to it as she gets to know Smoky Quartz, such as reffering to one of the voice actors and to Cartoon Network itself.
Tamatoa (Moana) is slightly aware that he is in a Disney film.
Control Freak (Teen Titans) is completely aware that he is in an animated series and has even found a way to reboot it which resulted in the creation of Teen Titans Go!
Mine's (akame ga kill) Wheel of pain (with gangan joker's mangas)
The Joker (DC Comics)
Card Collector (Valkyrie Crusade) is aware she is in a game, and even thinks that her power should be used on it.
Lincoln Loud (The Loud House) frequently speaks to the viewer as a means of coping with his large family, and eventually passed the secret on to his friend, Ronnie Anne Santiago.
On April Fools' Day, Luan Loud's (The Loud House) comedy becomes strong enough to break the Fourth Wall.
The Squid Baron (center) (Shantae series) is aware he lives in a videogame, which often rubs off on Shantae.
Frank Underwood (House of Cards) frequently blurts his ambitions to the audience, and no one's the wiser.
Elliot Alderson (Mr. Robot) often likens the audience to an imaginary friend.
While not fully conscious of their fictional nature, Rosencrantz and Guildenstern (Rosencrantz and Guildenstern are Dead) do possess a limited awareness of the absurd nature of the events that surround them.
From his actions and words, it is made clear that the Player King (Rosencrantz and Guildenstern are Dead) is aware that he, Rosencrantz and Guildenstern are fictional characters acting out a story on repeat.