I've only really noticed that black cats (like Felix, Sylvester, Pussyfoot, Mittens), tabbies (Garfield, Puss in Boots, Heathcliff) or Siamese cats are the mainly used breeds.
Black cats and tabbies aren't breeds. Just coat patterns.
As for actual cat breeds shown in animation, there are hardly any. Mostly the only two you see are Siamese and Persians. Every once in a while, you might get something else - I think the cat in "Over the Hedge" was a Himalayan but it's pretty rare.
I think that usually a long haired cat that doesn't have the body shape of a Persian can be seen as an Angora (like Duchess from The Aristocats) but even then, that's mostly a guess.
I always wondered what breed Selina Kyle's cat, Isis, was supposed to be in Batman: The Animated Series.
A little research online suggests it was possibly a Russian Blue, which I'd never heard of before. (Apparently, Isis is a Siamese cat in Krypto, but I've never seen it.)
Wow!! The cat in that first pic certainly does look like it could be Garfield. I also always thought Garfield was just an orange Tabby, but now that you bring it up, the Exotic Shorthair looks even more like him.