The user can make themselves turn completely flat with absolutely no depth whatsoever, allowing them to slide through cracks in walls, hide by standing sideways, stick to walls, and slide under locked doors. They can also choose freely shift parts of their body to become flat and sharp.
Ravio's bracelet (The Legend of Zelda: A Link Between Worlds)
Prismo (Adventure Time)
Teri (The Amazing World of Gumball)
The Folded Man (DC Comics)
Pancake Peggy (The Disrespectoids)
The Boneless (Doctor Who) are beings from a 2-dimensional universe.
Link (The Legend of Zelda: A Link Between Worlds) gained the ability to transform from corporeal form to painting form at will after being hit by one of Yuga's picture imprisoning spells whilst wearing a mysterious bracelet.
Val Ventura/Flatman (Marvel Comics)
Piper DaliPaper Doll (Marvel Comics)...
...can compress her body to a flat form...
...including doing so selectively.
Tommy (Marvel Comics)
Jiraiya (Naruto) using Toad Flat: Shadow Manipulation Jutsu.
Diamanté (One Piece) using his Hira Hira no Mi powers to turn his objects and himself into flattened states.
Elastigirl (The Incredibles)
Tom Turbo (Tom Turbo) can make himself flat to crawl beneath doors using one of his 111 tricks.
Flat Stanley (Flat Stanley) was flattened in bed by a bulletin board that fell on him in his sleep.