Detective Animal

He may be the Funny Animal, the Intellectual Animal, or maybe even the Speech-Impaired Animal, but if there's one thing that he's incredibly good at, it's solving any kind of mystery that comes his way. He can be either a Hardboiled Detective, an Inspector Oblivious, or a Defective Detective. Whether he does it on his own, or with a friend, or with a group of humans, expect him to help solve the case with ease.

Examples of Detective Animal include:

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Advertising PSA McGruff the crime dog has that whole Columbo thing going for him.

Detective Chimp from DC Comics.
In the few stories he narrated himself, Batman's dog Ace the Bat-Hound was shown to be an expert detective.

The Great Mouse Detective
That Darn Cat
In Oh Heavenly Dog, Chevy Chase plays a priveate eye who is sent back to Earth as a dog on order to solve his own murder.

In Anonymous Rex, a velociraptor in disguise as human is a Hardboiled Detective. (But the book is set In a World where there are dinosaurs living among us, so he's not unique.)
The title character of the Mrs. Murphy Mysteries.
Akif Pirincci's Felidae series features, as you might guess from the title, a cat detective who solves cat crimes. Not as silly as it sounds.
Three Bags Full by Leonie Swann is a murder mystery that gets solved by a flock of sheep.
The titular hero of the Basil of Baker Street series is a Mouse World version of Sherlock Holmes. These books were the source material for The Great Mouse Detective.
The Midnight Louie series of novels, Midnight Louie being a cat.

Slylock Fox is a puzzle strip featuring a fox who solves crimes while dressed as Sherlock Holmes. Most of the other characters are anthropomorphic animals, too.

Lancelot Link, Secret Chimp
Wishbone played the roles of Sherlock Holmes in "The Hound of the Baskervilles" and "Scandal in Bohemia" and C. Auguste Dupin in "The Purloined Letter".
The German Shepherd dog Inspector Rex from the eponymous Austrian crime series.

Team Chaotix from Sonic the Hedgehog.
Pennington from Paper Mario: The Thousand-Year Door. Though at the end of the chapter, he reveals he's not a real detective, he just likes to pretend.

Scooby Doo, most of the time.
Brain from Inspector Gadget.
Darkwing Duck, like his inspiration Batman, is a Badass Normal Animal Superhero who also does detective work from time to time.
Mumbly, though he is said to be an Expy of Muttley.
Clue Club featured two dog characters, Woofer and Whimper. However, Woofer is a bit of a Know-Nothing Know-It-All and Whimper is his Hypercompetent Sidekick.
Jabberjaw featured the eponymous shark who helped his human friends, Biff, Shelly, Bubbles and Clamhead, solve mysteries in a futuristic underwater world.
Subverted with Hong Kong Phooey, who may be "number one super guy", but the mysteries that he encounters are actually solved by his cat, Spot.
The Sylvester and Tweety Mysteries, though it's mostly accidental. The bickering among Sylvester, Tweety and often Hector causes clues to appear in front of Granny, who then solves the mysteries herself.
Snooper and Blabber are a cat-and-mouse detective team from The Quick Draw McGraw Show.
The Hunter from King Leonardo and His Short Subjects.
Perry the Platypus from Phineas and Ferb.
Danger Mouse. He's a secret agent but he still does yeoman's detective work.