Many traits associated with cats, including cleverness and contemptuousness (among others), tend also to be associated with Deadpan Snarkers — coming mainly from the association with cats as being aloof, unaffected, coming off as superior, and being associated with sense and grace. As such, it only makes sense that some works would have some cats be among their most sarcastic characters, whether as verbally-sarcastic talking cats or as Silent Snarkers. This could sometimes involve a cat as a Snarky Non-Human Sidekick.
Note that this trope isn't JUST about domestic cats, or even about cats that look like domestic cats either. It could apply to bigger cats as well.
Examples
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Anime & Manga
Both Luna and Artemis from Sailor Moon are masters of snark, especially when dealing with their respective less-than-devoted proteges.
Yoruichi from Bleach is quite sarcastic in her cat form... and her human form. Let's just call her a Deadpan Snarker in general.
While the title character from Kimba the White Lion is an Ideal Hero, he occasionally says a snarky line when he's talking with his enemies.
Bella Dona: Now tell me, Kimba: What happened to that turtle?! If you don't tell me where that turtle is, I'm going to... I'm going to... Kimba: You're going to be punished by Tonga for letting him escape? (smiles)
Toyed with in the "Nekotalia" strips of Axis Powers Hetalia. There are all kinds of cats there, but the only one who really fits in is Tama a.k.a. Japaneko... and that's when he's not ranting about tuna.
Cleo: 'Name me'? What do I need a name for? I am the best, how can anyone not know who I am? And you, what do you need a name for? You are so recognisable, you are unforgettable!
Simba: I'm gonna be king of Pride Rock! Scar: Oh goody. Simba: My dad just showed me the whole kingdom! And I'm gonna rule it all! Scar: Yes. Well, forgive me for not leaping for joy, bad back you know. Simba: Hey uncle Scar! When I'm king, what'll that make you? Scar: A monkey's uncle.
Mittens, from Bolt, is the character in the page image.
Bolt: I will Super-Bark you out of that tree! Mittens: Go nuts. Let's see how that works out for ya. (Bolt barks) Mittens: Oh, the super-bark. Scary, scary.
Morwen's cats, from the Enchanted Forest Chronicles, are practically an entire brigade of snarker cats. Morwen even notes that it's a good thing witches can only hear their own cats' comments.
Jon: "You know Garfield, I get the feeling you're a cat with a little cynic in you."
Garfield: "That's not true! I'm a cynic with a little cat around me."
Hobbes the imaginary and/or covertly-real (depending on how you interpret him) tiger from Calvin And Hobbes is arguably the most frequent Deadpan Snarker in the series.note Interestingly enough, author Bill Watterson claimed his pet cat partly inspired the portrayal of Hobbes, but he didn't specify whether or not this included the snarky personality.
Calvin: "Live for the moment" is my motto. You never know how long you've got! You could step into the road tomorrow, and wham, you get hit by a cement truck! Then you'd be sorry you put off your pleasures! That's why I say "live for the moment." What's your motto? Hobbes: "Look down the road."
Bucky from Get Fuzzy who, like Garfield, has a sidekick who exemplifies Dogs are Dumb.
Palmtop in Safe Havens has more or less settled into this role.
Theatre
Moppet and Poppet in the opera Paul Bunyan are snarkers in a philosophical way, quoting Peer Gynt.
Video Games
Sissel from Ghost Trick is certainly a snarker, though even he doesn't find out he's a cat until the very end of the game.
Another non-talking example would be Opal from My Little Pony: Friendship Is Magic. The timing of her meows and facial expressions combined give off this trope's feel. This applies especially well to Sweet And Elite, where Rarity keeps talking to Opal about various things and Opal almost constantly responds in a Silent Snarker type way.
Don't forget the time that Sweetie Belle wonders aloud if she could be good with animals. Opal slices off part of her mane with Audible Sharpness and smirks as if to say "Lol, U mad?"