When an average person is asked what superpower they'd most like to have, invisibility is a pretty common answer. While people in the real world can't become invisible, that doesn't stop invisible anime characters from popping up in all kinds of shows.
Anime characters with invisibility powers have different ways of manifesting their abilities. Some characters like Toru Hagakure of My Hero Academia is completely and permanently invisible, to the point of having no idea what she actually looks like. Other characters, like Absolom of One Piece, can turn their powers on and off at will. Still others, like Aizen of Bleach, don't actually turn themselves invisible but manipulate other people's minds to stop them from perceiving them.
Who is the best invisible characters from anime? That will be determined by your vote.
Invisibility isn't one of Sōsuke Aizen's most noteworthy powers, but he does make use of it from time to time. Being a Shinigami makes him invisible to human eyes, but he's also able to disguise himself when it comes to other Shinigami. He does this through hypnotizing people into not being able to see him, rather than by actually altering his own body.
Shizuka Joestar is a baby girl who Joseph Joestar found on the side of the road and then adopted. Because of her Stand, Achtung Baby, she is constantly invisible, and can only be seen when she's wearing clothing, makeup, and sunglasses. When she's scared or upset, she also turns things that surround her invisible, such as the hands of people who are holding her - but unlike her body, invisible objects that surround her go back to normal when she calms down.
Toru Hagakure has been invisible for her entire life, and she can't turn it off. As a result, nobody knows what she actually looks like. Her invisibility has limited application at first since it's hard for her to be particularly stealthy when she has to wear clothing that doesn't turn invisible with her. However, she learns to refract light off of her body, which can temporarily blind her opponents.
The Invisible Girl appeared at the end of Interviews With Monster Girls. While she doesn't have a name yet, it seems likely that she'll be an important character in any future seasons of the show. She reveals to Takahashi that while she doesn't know what she looks like because of her complete and permanent invisibility, she's had her portrait drawn by people who felt her face and made guesses about its appearance based on things like the shape of her nose and the arch of her eyebrows.