Richard Petty voiced one of the cars, named The King (a Shout-Out to his Fan Nickname). It's a Plymouth Superbird with a #43 on it (his most famous car), and on one race, it even crashes in a frame by frame recreation of his famous 1988 Daytona 500 crash.
Mrs. The King, voiced by Petty's Real Life wife, is depicted as the same car she used to drive to his early races, before he became famous.
Similarly, two cars in the film are voiced by Tom and Ray Magliozzi, hosts of the radio show Car Talk. At one point the film, they say "Don't drive like my brother!" "And don't drive like my brother!", their Catch Phrase on the show.
Mater says of tractor tipping "I don't care who you are, that's funny right there," a catchphrase of his actor Larry the Cable Guy. Also, when Lightning McQueen jets out of the pit in the final race, Mater shouts Larry's other catchphrase, "Git 'Er Done!"
In the sequel, Miles Axlerod apparently got his name from a joke his voice actor Eddie Izzard told involving the wheel and axle.
Also, when he says that he hails from the land of the free, one chicken asks expectantly: "Scotland?"
When he later becomes unpopular with the hens, one of them mentions: "I doubt he even was an American.", referencing the fact that Mel Gibson is believed by many to be Australian. (He is partly Australian, but very bitter about it.)
During his first scene with Buddy Pine, the future Syndrome (voiced by Jason Lee), Mr. Incredible forgets the boy's name. Incredible's first guess is Brodie, a reference to Lee's character Brodie Bruce from Mallrats.
Frozone's scene with the cop and getting the drink of water is a direct homage to Samuel L Jackson's scene as Zeus in Die Hard With A Vengeance, in which a cop is about to shoot him but he needs to answer a pay phone.
Antonio Banderas is well-known for his role as the masked caped crusader in The Mask of Zorro, as well as the cheesy line "you are the love of my life" which Puss in Boots (who Banderas voices) repeats to a female cat just before getting on the boat in Shrek Shrek the Third. Not to mention him carving a "P" into the side of a tree with his rapier, just as Zorro is known for carving a "Z" on his enemies.
King Harold makes a excuse about his old "crusade wound" acting up. As Basil Fawlty, John Cleese made a similar claim about an old war wound.
Sid has Buzz Lightyear (voice of Tim Allen) trapped in an upside-down plastic crate with a tool box on top. The tool box clearly sports a Binford logo; Binford Tools was the sponsor for "Tool Time" on Tim Allen's Home Improvement.
Earlier in the movie, Mr. Potato Head says "What are you looking at, you hockey puck?" causing a puck toy to shrug. "Hockey puck" is a famous insult Don Rickles uses in his comedy routines.
In Meet the Robinsons, a character is asked to describe the appearance of his father. Since the person asking him the question will grow up to be his father (it involves time travel) the character lies and claims his father looks like Tom Selleck. Later in the movie, the person meets himself as an adult, who is in fact voiced by Tom Selleck. (This was actually done in reverse: the line was written first, and that gave them the idea of offering Tom Selleck the role.) Worth noting is that in at least one dubbed version of the movie, they changed the joke to reflect the voice actor, despite a visual of Tom Selleck in the film itself.
Rapunzel is always portrayed as being barefoot, much like her voice actress Mandy Moore.
In the campfire scene, Rapunzel tells Flynn "Don't freak out!" and then "It's complicated!" in short order. Both of those lines are fromChuck, starring Zachary Levi, the voice actor for Flynn.
In The Rescuers, Miss Bianca is portrayed as representing Hungary. She was voiced by Eva Gabor, who was Hungarian herself. Moreover, there is at least one scene where Bianca mispronounces words; a reference to her Green Acres character Lisa Douglas.
In Chill Out, Scooby-Doo!, Shaggy, while messing around in the DJ studio, tries his hand at it. His VA Casey Kasem of course is well known for being a famous radio DJ.
Probably the earliest example, in Pinocchio, Jiminy Cricket hides from Gepetto by blending in with the players in a wooden music box and scatting along with the box's tune. His voice actor, Cliff Edwards, was known for his scat singing.
The title character of Kung Fu Panda makes frequent use of Jack Black's catch phrases, most notably "Skadoosh".
In Planes, two minor characters are Bravo and Victor, two Navy F-18s, who feel "The Need for Speed". The characters were voiced by Anthony Edwards and Val Kilmer, both of whom flew fighter jets in Top Gun.