All Animation Is Disney, naturally. Concerned entirely with the adventures of Mickey and Minnie, Donald Duck, Goofy, Pluto, Scrooge McDuck and his nephews. Sometimes Jiminy Cricket and Tinkerbell, too. And, uh, wasn't there a horse? And a cow?
And if a cartoon is referenced its style will be more typical of the Looney Tunes and Tex Avery cartoons.
Looney Tunes characters: Bugs Bunny, Daffy Duck, Porky Pig, Tweety Bird, Sylvester, Elmer Fudd, Yosemite Sam, Speedy Gonzales, Marvin the Martian, Wile E. Coyote, and the Road Runner. Anyone who can name a character other than that needs to get out more.
Hanna-Barbera characters: The Flintstones, The Jetsons, Yogi Bear, Scooby Doo...That's pretty much it. Few will remember that Hanna-Barbera did Tom and Jerry and The Smurfs, or live-action stuff like Kiss Meets the Phantom of the Park.
A short list of legendary animators whose mention will get you only a blank stare: Ralph Bakshi, David Silverman, Will Vinton, Richard Williams.
Notable exceptions and aversions of this trope from Western Animation shows:
Family Guy, lowbrow show that it is, occasionally allows Brian and/or Stewie to show their considerable knowledge of the arts - Brian was once enraptured by an old woman's rendition of "Habanera" and Lois deplored Peter's jazzed-up version of The King and I. It's perhaps the only show where you can hear the characters talking about Matisse, then hear a fart joke.
Lampshaded when Peter makes a remark about Benjamin Disraeli, and we cut to a cartoon version of Disraeli writing for several seconds before turning to the audience and saying "You don't even know who I am!"
Further lampshaded when Peter says that Kathy Ireland has betrayed him "worse than Lady Macbeth betrayed Duncan" - cut to a bear fighting Lady Macbeth on a spaceship - Peter says "I uh, I don't know Shakespeare very well."
Or how about single-handedly making "Shipoopi" from The Music Man into a viral YouTube sensation... thanks to an excessive touchdown celebration?
"Tales of a Third Grade Nothing"
Frank Sinatra Jr.: Hey, you girls thirsty? Could I interest you in a couple of Rob Roys?
Woman: What's a Rob Roy?
Frank Sinatra Jr.: Only the drink of Mr. Peter Lawford.
Bottom line, for all the references to huge pop culture phenomena like Star Wars that the show makes, it makes almost as many references to stuff that only a small portion of the audience would be familiar with, be it a forgotten old jazz musician or an obscure kids cartoon from the seventies.
In Anastasia, the characters attend a ballet; the performance is Prokofiev's Cinderella. This was a good choice on the part of the writers—even if only a few audience members were familiar with Prokofiev's ballets, it was immediately obvious from the costumes and props what the story was. Also notable is that the act's closing scene parallels Anya and Dimitri's relationship at that point; such an effect is not as easy to pull off when this trope is played straight.
The 80s children's stop-motion series Moschops had a variety of saurians, from Allosaurus to Icthyosaur. None of them ate each other, though Uncle Rex was a bit fierce.
And the main character was a Moschops? That is not a reptile anyone will have ever heard of without purposely doing the research.
Lisa: Bart, Pablo Neruda said, "Laughter is the language of the soul."
Bart: (irritably) I think I'm familiar with the works of Pablo Neruda.
One episode has Mr. Burns joking that the power plant's profit margins are "thinner than Louise Brooks' negligee". When Homer fails to respond, Burns is compelled to explain the reference. This is done, though, to show how much Burns is out of touch with recent pop culture.
Futurama gets a lot of humor from Fry's 20th century background, so a lot of the jokes aren't exactly obscure. But many of them are much more subtle and academic. Examples include Klein Beer (guess what the bottle looked like) being sold in a store advertising free bags of ice-9 and the holophonor, a recurring plot device based on the Visi-Sonor from the Foundation series (extra points for being possibly the only Foundation reference in mainstream pop culture ever). Also made jokes about orders of infinity (a cinema called aleph-0-plex, likely meant to one up "The Googlplex" cinema in The Simpsons) and the Heisenberg Uncertainty Principle's "observer effect" (scientists change the result of a horse race by observing it).
More Genius Bonus: Bender advertises his computerized dating service as discreet and discrete. In one episode a closet contains two boxes, P and NP, and a robot planet named Chapek 9.
In the commentary on one of the movie DVDs, they talk about one of their favorite gags was to throw in as many obscure mathematical references as they could.
Darkwing Duck managed to work in references to The Dark Knight Returns. It also has a villain named Taurus Bullba, a gag on Taras Bulba, a fictional Ukrainian folk hero and film starring Yul Brynner note And the Nikolay Gogol's novel, for crying out loud!.
How about that the engines on the air pirates' ship in TaleSpin are modeled on the one from Master of the World starring Vincent Price? Or that the Sea-Duck uses a version of the WWII-era overdrive system known as "war emergency power", in the multi-part pilot (Baloo burns it out, so they can have a cool scene without keeping around a potential story-breaker)?
Many of the episodes of Chip 'n Dale Rescue Rangers are named after Golden Age films that children wouldn't be aware of, and often contain some Parental Bonuses that may go over the head of a few adults. One particular episode was full of obscure references, including a possible cameo by a young Franz Kafka (or an Expy) and a reference to Ronald Reagan's autobiography.
The Tick features a character named "Die Fledermaus," a Batman pastiche dressed like a bat. The name doesn't make a lot of sense until you realize that it is German for "the Bat" and the name of a popular German operetta. Consequently, unless you speak German you need a working knowledge of light opera. And honestly, who can name a light opera not made by Gilbert and Sullivan? Not many, that's who.
The Batman 1960's TV series actually used a reference to Batman being called "Die Fledermaus-mensch" and helpfully explained what it meant, so no, you don't need to speak German or know opera to understand it.
Handy: "Even now, [the Tick] sulks like Achilles in his tent." [blank looks from everybody] "Achilles? The Iliad? It's Homer! READ a BOOK!"
ReBoot is naturally filled with references to computer technologies, many of them antique when the episodes were made.
Enzo * complaining about going to ancient language class instead of hanging out with Bob* :"COBOL? FORTRAN? They're dinosaurs!
Although Daria, being an MTV show, kept a fair handle on pop culture jokes in general, the eponymous protagonist had a great habit of referencing obscure, deep, and intelligent literature in relation to her present circumstances, most of which went right over audiences' heads.
In an episode of Phineas and Ferb, Baljeet imagines himself as "Hanumanman", a superhero modelled after the Hindu monkey god Hanuman, who plays a major role in the Indian epic poem Ramayana. Hanuman is well known in India, but how many western viewers had ever heard of him before?
If you saw the Sesame Street special in which Big Bird visits China, you'd recognize Hanuman as the Indian version of the Chinese "Monkey King."
The Ren & Stimpy Show features plenty of classical musical cues, some of which are not very well-known, like Chopin's "Ballad in F-Minor Op. 52", or Josef Suk's "Asrael" symphony, or Claude Debussy's "Canope", or Pyotr Ilyich Tchaikovsky's "Francesca da Rimini".
In one episode Henchman #21 wants to say "Sic semper tyrannis," which is what Abraham Lincoln's assassin was alleged to have said. He actually says "Semper fidelis tyrannosaurus," but Killinger does tell him what the right quote was.
In another episode, we get a lampshading of the trope when Phantom Limb tries to sell a stolen Rembrandt to a dumb sounding mobster. He claims he wants the Mona Lisa, which causes Limb to frustratedly remark that just because a painting is better known, that doesn't make it better.
Minor example, played mostly due to Rule of Funny. An episode of Duck Dodgers features a short appearance of a group of people referred to as the Presidents of the United States, consisting of the four LEAST known US presidents. Dodgers' reaction is understandable.