Sabrina, from the furry webcomicSabrina Online, subverts this by revealing that Sabrina is actually a Barefoot Cartoon Animal, and her ostensibly naked lower body is in fact covered with stretch-pants that match her skunk fur pattern. Her roommate, Amy, borrows some when she puts on weight during pregnancy.
Prior to the creation of the comic, Amy (who at the time was the creator's main character) was depicted wearing only a skirt. Yes, she had breasts, but they were somewhat vaguely defined and noticeably fuzzy, suggesting the traditional "they don't need clothes because the fur covers it" explanation.
This also occurred later on with Sabrina's boyfriend, who was a bit shocked◊ to find that Sabrina was buying underwear.
This gets turned Up to Eleven in a short animation featuring Amy jogging to her job... while forgetting something.
Ozy from Ozy and Millie generally wears a vest and a top hat, but no pants. Ms. Sokowitz and Avery and eventually Llewellyn have outfits that lack pants as well. Millie and Felicia do not wear shirts, and Millie has plenty of scenes entirely unclothed.
This is something of an odd example—it regularly draws comment, suggesting that Ozy and Avery is expected to wear pants, yet nobody ever treats it as if his exceptional nudity is a problem. Other characters his age also go around without a full complement of clothing with no comment. As is usually the case with this trope, calling attention to the fact is mostly based on the Rule of Funny.
Max and Cecil from Loserz usually go naked, but for a water fight, they wear trunks. This is lampshaded in this strip:
Cecil: "Omigosh! He's right! I feel so dirty!"
There were advertisements for Ctrl+Alt+Del shirts with Zeke, resident robot, exclaiming that "Wearing a shirt only draws attention to my complete lack of pants!"
The Fartmutant from Powerjeff, while not an animal, follows this trope. The shirt seems arbitrary seeing as how he spent the first few issues completely naked (but still PG) 
Sequential Art has half-dressed squirrel girls for the most part, once they're reminded that they don't need to be the Innocent Fan Service Girl squad. Kat and Pip are both fully clothed (unusual for a penguin).
Kevin & Kell usually avoids this for mammals and insects; they're expected to be fully dressed. Birds tend to be nude, although a 'bridesmaid dress' worn at an avian wedding looked more like a bird costume.
Some of the anthropomorphic animal characters in Exterminatus Now are fully dressed up in trousers or skirts, shirts, ties, shoes, boots, coats or trenchcoats, while others wear only a trenchcoat, or only a hat, or a sash plus boots and nothing else. At one point, one of the (pants-wearing) characters even comments on his (pantless) colleague's lack of trousers, who tells him to get lost. Of course, most of the characters have fur, or if they're turtles or mantis-people they lack outward sexual characteristics anyway. Clothing seem to be pretty much optional and just a fashion statement. No-one seems to be completely undressed, however.
"I don't need your standard-issue loincloth, I've been walking around without pants this entire time! It's called a genital sheath, look it up. Hey, while you're at it, look up 'hemipenes', because you can suck BOTH of my--"
Female dragons from Dragon City have all their naughty bits under their tails, so they normally run around naked, but when Erin joined the Dragoness Scouts, she and the other dragonesses had to wear green vests...and only green vests. Erin makes a comment that wearing the vest makes her feel naked.
Male dragons only wear shorts most of the time.
Kimbo from 1930 Nightmare Theatre is a textbook example, usually wearing only a shirt and nothing else. However, it's both lampshaded and subverted in this strip. (NSFW) Also, him and the other funny animals in the comic can apparently sport Sudden Genitalia when needed, and it's lampshaded more than once.
Very few characters in The Packrat are fully clothed, even most of the females and cameo celebrities aren't.