Faux Paw

A character is supposed to be imitating or acting like a cat, so he starts batting at a moving object with their fingers curled in to imitate the rounded look of a cat paw. Bonus points if he starts licking his faux paw. This move is often favored by Catgirls.

This move also doesn't actually make any sense if the person in question is supposed to be acting on actual cat instinct: when a real cat grabs at something, its digits will be splayed out as far as possible to maximize their grab capacity. Under other circumstances it does serve two purposes: it more closely mimics the shape of a cat's paw than a fingers-extended position does, and it reinforces that the person is imitating a cat, not merely swatting at a mosquito.

Anime & Manga

 * Tokyo Mew Mew: Ichigo bats and licks when she first becomes a Mew.
 * Ranma One Half: Ranma does this when his ailurophobia drives him into thinking he's a cat. Justified in that he's not actually supposed to be a cat or part-cat; he's just acting how he perceives a cat would.
 * Soul Eater: Blair in her human form. Strange, since she as a cat would stretch her arms out.
 * Botan from Yu Yu Hakusho does this when behaving "catty".
 * Matsuri and Miu, in episode 51 of Ichigo Mashimaro, each don kitty ears (not the kitty hat from episodes 8 & 43. Matsuri mimics does the Faux Paw maneuver (just batting, no licking), to Nobue's delight. Miu behaves more like a cat that's lashing out. Nobue doesn't think so highly of this.
 * Himari, the title catgirl of Omamori Himari, is quite prone to this, as seen here.
 * In K-On!, Azusa does this while donning cat ears, resulting in the other girls swooning over her (and giving her the nickname "Azu-nyan").
 * Hazuki in Tsukuyomi Moon Phase, especially in the opening. You can watch it here.

Comedy

 * Used in Jim Gaffigan's stand-up routine. "Just cause I make a hot catwoman... meow..."

Comics -- Books

 * Empowered as Schrodinger's Catgirl (in an Imagine Spot).

Live-Action TV

 * In Pretty Guardian Sailor Moon, Luna does this when she's in human form.
 * Big Wolf on Campus: An episode features a werecat who performs the Faux Paw maneuver.
 * Shoutaro of Kamen Rider W claims to be able to work out where a missing cat is the same way he finds missing people: by getting into the cat's mindset. He does so by performing a Faux Paw and meowing; not only does it work, but.

Theater

 * Used by performers in Andrew Lloyd Weber's Cats.

Video Games

 * Project Diva Extend: Hatsune Miku in the Nekomimi Switch PV.

Web Comics

 * Done by Ellen to Nanase's ponytail in El Goonish Shive several times starting here.