Gadget is more than obviously based on Jordan from Real Genius (though her design was actually based on a Disney storyboard artist named Lonnie Lloyd — including the jumpsuit!).
Word Of God has it that Fat Cat himself is modeled after Vincent Price, and that his goons Wart and Snout are references to Peter Lorre and Paul Lynde. On the other hand, another inspirational source for Fat Cat might have been Sydney Greenstreet who also stars in The Maltese Falcon, as is Peter Lorre. "Adventures in Squirrelsitting" was the episode which introduced Fat Cat, So Yeah...
Professor Nimnul has been proved to be modeled after one of the most important persons behind Chip N Dale Rescue Rangers, Bruce Talkington.
Stan Blather is a Shout Out to the news anchormen Dan Rather and Walter Cronkite.
Sparky from "Does Pavlov Ring a Bell?" is quite similar to Dr. Emmett L. Brown.
The recurring incidental characters Edgar and Chauncey from Rocky and Bullwinkle appear in "To the Rescue".
"Gadget Goes Hawaiian" was written around Deborah Walley to give her another character; it is a Shout Out to Gidget Goes Hawaiian in which she stars as the main character.
Monty's father Cheddarhead Charlie bears a striking resemblance to Mick Dundee.
Rat Capone is a Shout Out to both Al Capone and James Cagney. His henchmen, Arnold Mousenegger and Sugar Ray Lizard, are named after Arnold Schwarzenegger and the boxer Sugar Ray Leonard.
Irweena Allen from "Risky Beesness" is the result of an in-joke targeted at Irwin Allen's The Swarm. And then there's still the obviously British heavy metal band Iron Goose.
The movie shown at the Drive-In Theater in "Good Times, Bat Times" bears a few striking similarities to Casablanca.
In "Dale Beside Himself", Dale watches a movie very similar to Alien which Monty describes as "a real ripper", maybe a nod to Sigourney Weaver's character name and what happens to John Hurt's character. Dale also watches something looking a lot like a Ed Wood movie on another occasion in the episode. The Fleeblebroxian shape-shifters could be a nod to John Carpenter's The Thing (1982). And on the Fleeblebroxian ship, Dale says the Star Trek: The Original Series quote-that-is-none, "Beam Me Up, Scotty!"
The Pi-Rats' first mate Jolly Roger shares his name with the famous skull & crossbones flag, and their disappeared captain Long Lost Lafitte is a play on Jean Lafitte. They have to deal with a certain Billy the Squid, a play on Billy the Kid.
"Pound of the Baskervilles" introduces the late detective novel author Lord Howard Baskerville and his character Sureluck Jones. All one big Shout Out to Sherlock Holmes in general and The Hound Of The Baskervilles in particular. One scene in this episode shows Howie Baskerville tear the interior of one of the rooms of Baskerville Hall apart in search of Howard Baskerville's last will which is somehow reminiscent of The Conversation.
The spaceship crew in "Out to Launch" are references, too, namely to the city of Houston, Texas, home of the NASA (Roger Houston), Edwin "Buzz" Aldrin (Buzz Airfield), and Sally Ride, the first American woman in space (Joy Rider).
Another Shout Out to Real Life would be the gorilla Kookoo and her kitten Boots in "Gorilla My Dreams", being references to Koko, the famous gorilla who could communicate with humans, and her kitten companion All Ball.
The show contains lots of Shout Outs to other Disney works: Humphrey the Bear from several Donald Duck cartoons has a Cameo in "Bearing Up Baby", the crocodile in "Kiwi's Big Adventure" was taken straight out of Peter Pan, Colonel Hathi and his elephant squad make an appearance as Captain Kernel & company in "An Elephant Never Suspects", the Siamese Twins have look-alikes in Lady and the Tramp, and last but not least, there is Detective Donald Drake and his police dog Plato (Donald Duck and Pluto).
Speaking of Dale in "Le Purrfect Crime", the large coffee bean container on his back gives his gun, the Decaffeinator, not little resemblance to Old Painless from Predator. Genius Bonus: Early Gatling cannons were crank-operated, as is the Decaffeinator.
The red dress Gadget wears as part of her Femme Fatale disguise makes her very reminiscent of Jessica Rabbit.
Henchman: Whatever. You chipmunks all sound alike.
Parts of "Chipwrecked Shipmunks" are quite reminiscent of Disney's rendition of Treasure Island.
"Battle of the Bulge" contains a reference to "the most tip-top Top Cat".
Wart: You're the most tip-top, Fat Cat!
Flash the Wonder Dog from the eponymous episode may be a nod to Thunderbolt from 101 Dalmatians.
The episode "Last Train to Cashville" is named after The Monkees' song "Last Train to Clarksville".
"Zipper Come Home" is based off of Lassie Come Home. See also Tropey Come Home, their common trope.
The Lucitetania in "When You Fish Upon a Star" is a reference to the RMS Lusitania, both of which sunk. Of course, the precious fish Moby Carp is named after Moby-Dick.
In "They Shoot Dogs, Don't They?", Monterey Jack and Canina La Fur do an obvious Shout Out to The African Queen on their boat. Canina's rival, Zsa Zsa Labrador, is a nod to Zsa Zsa Gabor.
Both Chip and Dale try and fail to kiss Gadget at the end of "Gadget Goes Hawaiian" much like they did at the end of "Two Chips and a Miss" (also known among fans as Episode Zero).
Heinrich von Sugarbottom from "Chocolate Chips" is basically Oliver Hardy in lederhosen, a nod to Laurel and Hardy. Another one out of many is Dale's "Hey, what's the big idea?" Yet another one is the deep puddle in "Chipwrecked Shipmunks" into which Jolly Roger sinks much like Oliver Hardy.
In the scene in "The Pied Piper Power Play" which infamously depicts Dale way out of character stupidity-wise, he mentions a certain Moonwalk Jackson, a reference to both Michael Jackson, his most famous dance move, the Moonwalk, and possibly also to his movie Moonwalker. Furthermore, Dale says the case would be a thriller, referencing Michael Jackson's best-selling album.
Aldrin Klordane, the Big Bad from "To the Rescue", is likely to reference Mr. Jones from Animal Farm.
Muscles, Errol's only henchman with a known name in "Love Is a Many Splintered Thing", is a Shout Out to Rocky Balboa.
The tunnel-digging mechanical dragon built by the two pandas in "An Elephant Never Suspects" might count as a (yet another) Shout Out to Dr. No which features a truck made up to look like a scary, fire-breathing dragon commandeered by a Chinese Big Bad.
The ring from "Throw Mummy From the Train" is a reference to The Beatles' Help! movie. The villain in the same episode, Wexler, is modeled after the Rescue Rangers staff member Ed Wexler. See the Norton Nimnul/Bruce Talkington connection above.
"Song of the Night 'n Dale" is a Shout Out to the Hans Christian Andersen fairytale The Nightingale; it also seems to reference The Cretan Bull from Agatha Christie's The Labours of Hercules.
"Ghost of a Chance" borrows a lot from the 1961 movie The Pit And The Pendulum, based on a work by Edgar Allan Poe, especially the namesake death trap.
King Kong is referenced twice: once by giant Zipper climbing up a skyscraper while holding Nimnul in "Fake Me to Your Leader", and probably once more by the aforementioned gorilla Kookoo climbing up another high-rise building in "Gorilla My Dreams".
In "The Case of the Cola Cult", the main plot plays out like the plot of Indiana Jones and the Temple of Doom (minus the heart-ripping of course) and the action scenes are similar.