Gumball and Darwin's mother, Nicole, has a lot of furry fans. That's not to say Gumball himself doesn't have those either.
Penny was originally this back when she was still inside her shell. Most fan-artists thought she'd be a cute looking moose character. She instead turned out a yellow shapeshifting fairy-like creature. Even then, this hasn't lessened the furry interest thanks to her true form looking pretty appealing and well... the fact that she can shapeshift.
Jake's dragon form in American Dragon: Jake Long is this, specifically his season 1 design since his season 2 design is less popular due to being less stylized and skinny, instead of muscular and winged. Rumor is that he was created by a scalie. Jake also attracts many Transformation Fiction fans because he can turn into a dragon. (Or maybe it's the other way around?)
Amphibia gained popularity with amphibian lovers in its first year of broadcast alone.
Angelina Ballerina is a preschool-aimed book series with two TV adaptations (Angelina Ballerina and Angelina Ballerina: The Next Steps) about a ballerina mouse in Slice of Life plots, but it has garnered a Periphery Demographic of mouse furries and people who like ballet. Both TV series have been the Gateway Series for some furry fans.
Though the character Minerva Mink is the focus of only two cartoon shorts in the original show, she's nonetheless an object of affection among furry enthusiasts. That Minerva appears in a Sexy Silhouette scene in each one tends to be her key attractant. The Warner Siblings themselves are a more minor example.
The reboot has no shortage of these either. Two particularly notables ones, Julia the mouse and Benedict the dragon, have found great success with furries and scalies, respectively, for their designs and personalities (Julia for being a Nice Girl who eventually turns against Brain, Benedict for being a Large Ham wannabe thespian).
The reboot's parody of Groundhog Day with Pinky and the Brain in the third season includes a direct Shout-Out to the furry fandom, with Pinky donning a disguise as a woodchuck and asking Brain if he should be "more furry." To which Brain responded with a "careful, we are already treading a fine line with that part of the fandom here."
The Arthur fandom is unusually split between those who are furries and those who aren't furries, but it still gets ton of fan work and fan fiction from furries.
Some of the Mutated Arkham Inmates from Batman vs. The Teenage Mutant Ninja Turtles are rather well-liked by some furries, for being well... being mutated animals of course. Hyena Harley Quinn is especially popular.
The Bellflower Bunnies has attracted a good amount of furries due to its main characters being a family of cute bunnies.
Blazing Dragons and its game version both have a huge cult following, in part thanks to the furry fandom. Many members of the Blazing Dragons fandom are also scalies or regular furries.
The Bluffers would have been entirely forgotten if it hadn't been for furries. Sharpey is the most popular member of the Bluffers among furries, being a fox and all.
Bravestarr is a cult-classic with a relatively small yet dedicated fanbase. A large portion of that fanbase being furries due to a prominent anthropomorphic cast. Especially Thirty-Thirty, a large and muscular cyborg-horse who totes a giant laser rifle and can transform between a four-legged horse and a two-legged anthropomorphic horse. There's also the Dingoes (a villainous gang of anthropomorphic coyotes who frequently cause trouble for the heroes) and Vipra (a recurring villainess who's a human-snake hybrid).
Capitol Critters has a cult following thanks to furries discovering the series when it was rerun in the mid-to-late 90s. Had it not been for the furry fandom, it would have been doomed to reside on "Worst TV Shows of All Time" lists along with the other early 90s primetime animated shows that tried to compete with The Simpsons.
Captain Simian and the Space Monkeys appeals to monkey-loving furries. Shao Lin in particular has a lot of fans, thanks to being a beautiful Action Girl monkey (specifically, a Chinese golden monkey).
A lot of Care Bears fan-artists are also furries. The series also has heavy Sailor Earth potential, making it popular with people who like OCs.
The Chip 'n Dale: Rescue Rangers fandom contains a lot of furries, many who consider the cartoon their Gateway Series. Especially Gadget, who is a fan-favorite (Disney was honestly surprised with her popularity).
And the One-Shot Character Foxglove, whose following is such you'd think she was one of the leads.
Another popular character who was only seen in a single episode is DTZ, the shapeshifting alien. His default form within the fandom tends to resemble the dragon form he has in the show.
Dora the Explorer has a decently large cast, with some of then being Funny Animals or at least intelligent animals. Boots the Monkey, being a cute monkey, appeals to the few monkey-loving furries out there. Then there's Swiper the Fox, whose appeal pretty much speaks for itself.
Dragon Tales is about two (later three) kids who use a magical trinket to teleport to another dimension populated by dragons. Naturally, it has a lot of furry fans, especially those of the scalie type, with Zak & Wheezie and Cassie getting the most attention. Some scalies have treated it as their gateway into the furry fandom.
Many fans of The Dreamstone are also furries. Rufus and Amberely seem to be the most popular characters of the show amongst the furry fandom.
The Droopy cartoon "Sheep Wrecked" has an unnamed female sheep nicknamed "Leggy Lamb" who gained popularity on the Internet in The New '10s. Her popularity in the furry fandom only increased after being prominently featured in a fan animation of "Beep Beep I'm A Sheep".
The majority of the small fanbase for Eckhart is comprised of furries. The titular character and his friend Bridget appeal to mouse fans.
Final Space has Avocato and his son Little Cato, who are easily the Ensemble Dark Horses of the show, especially with the furry fandom.
This series gets a lot of love from furries, especially Brooklyn. The Mutates also get a bit of love, and the Avalon world tour demonstrates that gargoyles as a species can look like just about anything your imagination desires.
Elisa is already very easy on the eyes, so when she temporarily turned into a gargoyle, you can bet her being returned to normal by episode's end was seen as a tragedy by some.
The Get Along Gang has a lot of furry fans (it helps that the show takes place in a World of Funny Animals), and probably would have been doomed to be remembered as "The Complainer Is Always Wrong: The Cartoon" had it not been for furries (re)discovering the series. Dotty Dog is the most popular member of the Get-Along Gang among furries, while Zipper Cat and Woolma Lamb also get attention from feline and lamb furry fans respectively. Moose furry fans also tend to like the gang's leader Montgomery Moose.
Peg from Goof Troop along with the movie characters Roxanne, Beret Girl, and Sylvia have a lot of furry fans (not helped by the fact Roxanne barely looks like a dog). Max's cousin Debbie and Mrs. Pennypacker also have fans. PJ and Pete have their fans too, especially when the LGBT Fanbase is taken into account.
Cleo and Wordsworth from Heathcliff & the Catillac Cats are popular with furries. The show itself was a Gateway Series for early furries, and Cleo is notable in that she's known as one of the "original" furry crushes.
Horseland is popular with horse fans and horse furries thanks to its focus on talking horses.
The French cartoons Kangoo and it's spinoff Kangoo Juniors have a following among kangaroo fans within the furry fandom. They would have been forgotten outside of France had it not been for the furry fandom.
Legend Quest: The character Alebrije has a small following among furries, scaly fans, in particular, have a soft spot for him.
Little Bear was a Gateway Series for some furries who grew up in the late 1990s and early 2000s, and as a result, has a small but good-sized following of furries.
Looney Tunes is huge with furries to the point where many accuse newer incarnations as being made for furry appeal, particularly the characters of Bugs Bunny, Wile E. Coyote, Pepé Le Pew, Penelope Pussycat, and Sylvester. Then there's Lola Bunny, who is much more humanized and most likely an attempt to aim at this. Her redesign and personality change in The Looney Tunes Show is less popular with furries (though by no means ignored, and also picked up some fans for her mother Patricia), but is in turn more popular with her detractors, though it's unknown if that will stick.
Mao Mao: Heroes of Pure Heart has a substantial furry following thanks to its slick animation, endearing characters, appealing art style and a cast entirely made of Funny Animals. While the titular character and his uncharacteristically masculine voice have earned him followers, Badgerclops, Tanya Keys, and Snugglemagne have proven to be almost, if not just as popular.
Similarly to Josie and company, Miraculous Ladybug doesn't actually feature animal-people, but a show with an ever-increasing number of cute human characters in animal-based costumes has not gone unnoticed! Especially popular is giving the characters animal traits (an Adrien who becomes putty in your hands if you scratch the right spot behind his ears and a Marinette who needs extra snuggles in winter because she's vulnerable to cold since actual ladybugs hibernate in winter are a perfect combination) or drawing what they would look like as anthropomorphized animals.
The relationship between the My Little Pony franchise and furries is complicated. Traditionally the fandom had no issue with furries. Many older fans are furries and the ones who aren't either don't mind or ignore it. My Little Pony: Friendship Is Magic and its large Periphery Demographic of young men is when the controversies began. Hype Backlash caused many furries to hate bronies, while in-turn many bronies insist that they aren't furries and hate furries. In contrast to most pre-G4 fans, many FIM fans don't even like horses. (They only like FIM ponies; part of it is the designs. There being more stylized and "cartoony" than their somewhat horsier predecessors means even slightly more realistic proportions make for a jarring step away from your cartoon crush and toward livestock; even when painted purple and given a cutie mark, your average anthropomorphized horse is still a few hoofbeats too far in that direction.) Which makes them more averse to other horse works and the furry fandom as a whole. There was at one point a huge Fandom Rivalry between bronies and furries. Still, many bronies consider themselves furries and some even make fan-works of the characters as human(oid)s (though it's often the cause for a Broken Base even amongst furry bronies). In the early days, it was also common for furries displeased with the fandom's internal politics to regard MLP as an alternative community.
Friendship is Magic features Spike and Ember, two dragon characters who are popular with scalies. The teenage dragons (Garble and his friends) are also popular. Ember in particular has a more humanoid shape than most and a classic Tsundere personality, winning her instant widespread adoration.
Fluttershy's bat form ("Flutterbat") is very popular amongst people who like vampires and people who like bats.
Popular fanon has Luna having a guard filled with 'bat-ponies'. These bat ponies are very popular. In canon, however, it's never been made clear whether they were just pegasus dressed up for Nightmare Night or not; we only see them on two occasions (Luna's Big Entrance in Luna Eclipsed, and in an Alternate Timeline, Nightmare Moon's guard - which includes the usually-very-much-not-a-batpony Rainbow Dash. While it's fun to imagine, the evidence seems to point away from a whole species of thestrals.)
The Diamond Dogs species have a following amongst dog fans.
Griffons always had a following due to Gilda, but they received a boost after more griffons began appearing. Even Posthumous Character King Grover, with plenty of fan drawings based on what he might've looked like based on his statue, has a following. On top of that, Gilda returned and Took a Level in Kindness but without losing her tough personality, and if she's still too gruff for you, there is now the sweet and adorable Gabby!
A few furries took a liking to Max the crocodile from Oddballs for his quirky personality and background. Even though his popularity waned a bit after he was revealed to be a schoolkid (not helped by the voice direction for him that misled people), he still proved to be one of the better characters out of the cast.
PB&J Otter is a preschool show about animals living on a lake, yet it has gained a cult following among furries, especially otter fans. The titular otter trio has a lot of fanart, and Opal Otter (the trio's mom) has a few fans.
The Raccoons is considered to be an influential Gateway Series in the fandom, and naturally has gained a lot of fanart from furries.
Regular Show obviously because half of the core cast are anthropomorphic animals. Other creatures that exist in this world are; humans, mythological creatures like yetis, unicorns, and centaurs, ghosts, and living inanimate objects like Benson who's a gumball machine.
With the many characters that reside in the Rick and Morty universe, there's quite a few furry/scalie/beast-like ones whom have garnered interest in the fandom.
Rabbit Morty from Pocket Mortys has naturally garnered a furry interest thanks to being a pretty adorable biped rabbit version of Morty, though his evolution isn't as popular.
Scaredy Squirrel has gained itself a not-so-insignificant number of furry fans, thanks to being set in a World of Funny Animals. The title character in particular is quite beloved by these people.
Catra, the Ambiguously GayCat Girl that takes place of The Heavy in the story and has strong UST with the protagonist has gathered a few furry fans.
On the scalies side, Rogelio, the silent and buff reptilian member of the Elite Mooks in the Horde, has also gotten some fans. The fact that he is also Ambiguously Gay with Kyle also helped with implications that they may be a couple.
Simsala Grimm: The show's main characters Yoyo, a blue coyote, and Doc Croc, a striped lizard, have gained a following among furries.
Storm Hawks: There are quite a few furry fans drawn to the various Beast Folk who populate the setting, particularly the Blizzarians (blue-furred canine-rabbit crosses), the Merbs, and the Raptors.
SWAT Kats has a following amongst furries. In addition to the two main characters, Deputy Mayor Callie Briggs is hugely popular with the fandom.
Rebecca, Baloo, Don Karnage and several of the Girl of the Week characters from TaleSpin have followings.
Both ThunderCats (1985) and ThunderCats (2011) are popular due to the protagonists being cats. The remake tends to be more popular with furries due to the characters looking more cat-like, though the original series is overall far more popular.
Toad Patrol has many amphibian lovers, scalies and furries in it's fanbase. Beauty Stem, Shaggy Mane, and Cleopatra the Skunk have attracted quite a lot of furry fans.
Tiny Toon Adventures, like its predecessor, attracts a good chunk of furry fans. Especially Fifi Le Fume, who is literally Pepe Le Pew as a girl.
While it's a series that focuses on giant transforming robots aliens, the Transformers franchise has it's fair share of furry fans over the years thanks to several factors:
The Dinobots from The Transformers — who are already quite popular in their own right — have scalie fans, while G1!Ravage has feline furry fans.
Beast Wars and it's sequel series Beast Machines would introduce "Beast Modes" but also have robot modes that are decently animalistic in their own rights.
To a lesser degree because of the level of cartooniness and the beast-bots' more alien designs, Transformers: Robots in Disguise (the 2000 series).
Transformers: Robots in Disguise (2015) has a decent amount of furry fans due to most of the Decepticons being very animalistic, with it's incarnation of Steeljaw being the most popular, thanks to his robot mode being very wolf-like.
Kitty is especially popular for her tight leather clothing and Hartman Hips (fitting, considering the show's creator), though slowly taking her over in popularity is her own mother: "Mrs. Katswell", because... well, she's Kitty's mother and already seems a bit curvy.
Dudley Puppy himself is also rather popular, especially amongst the MLM crowd thanks to his somewhat endearing dumbness and hisbuild, both of which make him look very himbo-like.
We Bare Bears is a slice of life cartoon about three bear brothers. It doesn't have as large a fandom as other contemporary Cartoon Network shows, but it still has one. Quite a lot of fans are furries as well. It also helps that it introduces other anthropomorphic characters, especially in it's Spinoff Babies show We Baby Bears thanks to Wolf.