Mice: From Disney. Morty and Ferdie. From DC comics funny animal books, Little Cheese of the Zoo Crew. From Warner Brothers, Speedy Gonzales.
Ducks: From Disney, too many to bother mentioning just in Ducktails and Darkwing Duck. From the Zoo Crew again, Rubber Duck. From Warner Brothers, Plucky Duck, and Duck (of Loonatics Unleashed).
Cats: From Disney, Pete (nemesis of Mickey and Goofy). From the Zoo Crew, Alley Kat Abra. From elsewhere, Garfield, Heathcliff, Stimpson J Cat. On the adult side, Omaha the Cat Dancer.
Dogs: Goofy is technically a dog. WB has Sam Sheepdog. And multiple bulldogs. Ren Hoek (chihuahia). From the Zoo Crew, we have Yankee Poodle.
Skunks: From WB, we also have Fifi LeFume (the Tiny Toons inheritor of Pepe’s role.)
Alligators: Wally Gator. One of the Mighty Mutanimals (Teenage Mutant Ninja Turtles allies) was an alligator. Wikipedia tells me his name is Leatherhead.
Just off the top of my head… Pete Puma, vultures out the wazoo, the Dodo bird, the Tasmanian Devil, Wile E Coyote, the Roadrunner (and their Tiny Toons equivalents), Tweety Bird (a canary), Woody Woodpecker, Woody’s walrus neighbour, various wolves (Big Bad Wolf, Ralph Wolf (friend and nemesis of Sam Sheepdog, all at once))… Rabbits - Bugs Bunny, Roger Rabbit, Captain Carrot (AKA Roger Rodney Rabbit of the Zoo Crew). Turtles - the Teenage Mutant Ninja Turtles, McSnertle the Turtle (AKA the Terrific Watsit), Fastbak (of the Zoo Crew again). Fox and Crow (a pair of DC comics funny animal characters). Pigs - Porky Pig, Petunia Pig, Peter Porker, the Amazing Spider-Ham, Pig Iron (of the Zoo Crew), Orson Pig, Miss Piggy (she was animated in Muppet Babies). Lanolin the Sheep. Mondo Gecko. Sandy Cheeks (Squirrel). Man Ray (several characters by that name - all rays, usually mantas). Mr Krabbs. Squidward Tentacles. Ray Fillet (also one of the Man Rays - he’s a manta ray, duh). Rocksteady (rhino), Bebop (warthog), countless foxes. Countless lions. Balloo the Bear. Louie the Chimpanzee. Sir Hiss (snake). Frogs - Kermit, Frogzilla. OK, I’m going to stop now. Even without racking my brain, this paragraph is insane, and if I actually gave it some thought, I could probably list hundreds without breaking a sweat. Or even leaving Disney and Warner Brothers, for that matter.
The Mr Hell Show had a seal (although I don’t know if he was a harp seal or some other species…it was unimportant) who was on a mission of vengeance against the people who clubbed his parents to death. (Unfortunately, he didn’t know who did it, so he went postal on pretty much anyone he encountered. ‘Eet wass yoooouuuu!’)
There’s a couple WB cartoons featuring a flea. (‘Food around the corner, food around the corner, food around the corner, for me!’)
You do pretty much have to go with something really odd to have something that hasn’t been done. And even then…you’re probably not going to be the first.