Archie Comics' Sonic the Hedgehog has Sonic's pet dog Muttski, one of the very few non-anthropomorphic animals seen in the comic (which also contains Funny Animal dogs). Tasmanian Devils are explicitly described in one issue as "One of the few Mobian races that never fully evolved", but Muttski doesn't appear to be one.
Which is later thrown out the window in a later story arc in which we DO have an anthropomorphic Tasmanian Devil fighting alongside Sonic and co. (It's hinted in-story that he may be an "experiment").
A Knuckles story arc prior to the reboot involves a fully evolved Tasmanian Devil who claimed that the reason other devils never fully evolved was actually due to the Echidna race's genetic tampering, and as revenge, stuck all of them but Knuckles into the negative zone (once again making Knuckles the only surviving member of his species.) This was the first attempt at putting several of Ken Penders' characters on a bus.
Following the reboot, Muttski is now a full-fledged Mobian, and his full name is now Ben Muttski. Sonic and Tails were shocked to discover that to say the least.
The Autumnlands: Tooth & Claw: Dusty explains that in The Autumnlands there are humanoid animals like himself and there are the 'unshaped ones' which seem to be normal, non-anthropomorphic animals. The nature of this relationship has yet to be divulged.
Bamse has this to some degree. There are anthro animals and non-anthro animals. To further confuse the issue many of the non-anthro animals are Non-Morphic Talking Animals (although mostly among themselves) oddly enough someone obviously thought about the Inter Species Romance aspects: Fox-girl and badger-boy mention that it would be nice if they were of the same species and then kiss despite this. (Then they get an apartment together, though both insist that they're still Just Friends. Draw whatever conclusion you like.)
In the French comic De cape et de crocs, everyone is human except for several characters who are anthropomorphic animals for no explained reason — most notably, the main characters who are a wolf and a fox. The writer is aware of the "chicken-man eating fried chicken" wrongness and plays with it a few times, but the more memorable one happens when the heroes almost get cooked by an indigenous tribe. They manage to free themselves and run into the chief, who realizes that they're not really animals, apologizes and invites them to dinner. He later explains that the villagers "misjudged them", at which point the wolf notices a man with a big knife leading a regular dog away from a crying child... then the dog cries out offscreen and the wolf looks down at his food with a horrified look on his face. The fact that he knew an anthropomorphic dog in canon only makes it more twisted.
Chilean comic book character Condorito has an anthropomorphic Condor as protagonist. Weird thing is Condorito also has two pets; a dog and a parrot.
The Mickey Mouse comics also have the current page image on Eek, a Mouse!!, which is Minnie Mouse saying the quote.
Howard the Duck, who comes from a world/alternate dimension (depending on the continuity) where mallards are a dominant species, is often shown reacting to the non-anthropormorphic ducks of planet earth. The film version adds a Nightmare Fuel aspect by having him Freak Out upon seeing someone eating eggs.
Done disturbingly in the Looney Tunes comics. One story has Bugs and Elmer wanting to make money and being told that selling animals fur is a good idea. Bugs goes off and immediately traps a huge cage full of non-anthropomorphic minks. A second later, he notices a carrot dangling from a tree and ends up falling into one of Elmer's rabbit traps. Elmer's been hunting too and has a cageful of ordinary, non-anthropomorphic rabbits. If this isn't strange enough, Elmer decides to capture Bugs as well, despite them being more or less friends (in the comics, at least), and then decides to throw Bugs into his OWN cage full of angry minks that proceed to attack the rabbit while Fudd happily watches. A police officer ends up arresting Elmer. No, not because he endangered someone's life and had basically kidnapped a sentient rabbit; Elmer is actually arrested because rabbits aren't in season. Wow.
Lampshaded in Art Spiegelman's Maus, where Jewish characters are depicted as anthropomorphic mice, while Germans are cats. At one point the main character is at the home of someone who keeps several dogs. For those panels, the characters are depicted as people in mouse masks and the author leaves a little note basically acknowledging that the metaphor falls apart for a moment there.
At one point inside the story, Vladek and Anja are residing in a basement when Anja freaks out over finding a legitimate rat.
Red Shetland brought up the topic in a conversation between the eponymous character (a Red Sonja parody) and her Sidekick Du Jour Eeon, who was a normal pony transformed by evil druids into...well, an anthro war-pony. Crazy druids, go figure. Red has no problems riding a horse, which she's on at the moment, and asks why Eeon doesn't ride, to which he responds "on my oppressed brethren?!".
In the furry comic, Rhudiprrt Prince of Fur, the title character, a human whose spirit was place in the body of a humanoid cat body in a world that is the realm where the spirits of deceased cats go after death in our world. At one point, he receives a pet animal that resembles a dog and Rhudi wonders with some amusement about where the spirit of that animal will go after its death.
Borderline Lampshade Hanging in the comics, where an ordinary, non-anthropomorphic dog in the background of a panel has a head identical to Sam's, complete with hat.
In The Devil's Playhouse (Season 3 of the Telltale game series), we're introduced to Sal, a cockroach. But Sam's dialogue reveals that cockroaches are actually used in the recipes of the place where he used to work as a fry cook.
Sometimes lampshaded in The Spiffy Adventures of McConey by the French comic artist Lewis Trondheim, where all characters are anthropomorphic animals. In one episode our heroes go on a search of a missing pet dog (a real dog, not an anthropomorphic one!) for whom a reward has been offered. When they watch a picture (which is not shown on the panel) of the missing dog and his owner, one of them asks: "So, who is the dog?" and another one answers: "The more short and less hairy one."
Usagi Yojimbo is set in an alternative feudal Japan populated by all kinds of anthropomorphic animals. The only major exceptions apart from birds, fish, and insects are horses (which are just the same as our Earth horses) and a species of long-necked lizard called "Tokage" ("reptile" in Japanese). On the other hand, the main villain, Lord Hikiji, is an altogether different kind of animal — he is the only human in Usagi's world.
Early in the series, humans appeared the background, and there have been cameo appearances by human guests from other comics a few times. It's possible that Stan Sakai regrets having any human characters established, but a retcon isn't happening... but then again Hikiji's face hasn't been shown since that one time in volume 1, and the latest Usagi RPG lists his species as "unknown."
Some animals that are considered to be Youkai in Japanese mythology, such as foxes, cats, and tanuki, occasionally appear in non-anthropomorphic form even though there are several antho characters of those species. Particularly confusing is a recurring character named Kitsune, who is an anthropomorphic fox named after the trickster spirits but not one herself.