Name in Japanese (translation): Paper Paper Fruit
Capabilities: The user of this fruit has the power to produce, control, and transform into sheets of paper. The paper can be used to slice up victims with paper cuts, or even crush them under the weight like a stack of newspapers.
Of course, this also makes the user extremely vulnerable to fire and other such burning attacks.
If the user gets wet, their body gets soggy and has its strength severely diminished, as well as the level of which they can control their paper until they dry off again.
Type: Logia
Note: Apparently this Fruit actually appeared in one of the One Piece video games, but I'm not sure if we're counting games as canon or not, so I put it up for application anyways.