Back in 1972, The ABC Saturday Superstar Movie anthology series featured Looney Tunes characters in a Filmation production, Daffy Duck and Porky Pig Meet the Groovie Goolies — an atypical crossover of characters from different animation studios. (Consider that veteran WB animators, such as Ted Bonnicksen, Virgil Ross, and Norm McCabe, were all working at Filmation at the time.)
Another King Features example: The main characters of Defenders of the Earth (King's action/adventure heroes Flash Gordon, The Phantom and Mandrake the Magician) were all from previous series, making the entire series a Crossover.
The Ben 10: Omniverse epsiode "T.G.I.S." sees the title characters of The Secret Saturdays appear, teaming up with Ben and Rook. Unlike the crossover with Generator Rex, the team-up is presented as (as per Word of God by Jay Stephens, the creator of TSS) as them existing in the same universe.
There's one line of promos they did called "Perfect as It Is", which show that certain cartoon character cross pairings just don't work out right. Take a look at "Tom and Speedy" (there was also "Road Runner & Dexter" and "Batman and Inch High Private Eye".
The Simpsons is confirmed to have had crossovers with Family Guy and Futurama.
The Family Guy episode The Simpson Guy has the Griffins go on a road trip and end up in Springfield, where they meet and befriend the Simpsons. Then Homer and Peter start a fight (a la Giant Chicken) over which beer is better and nearly destroy Springfield.
A crossover of Darkwing Duck with Chip 'n Dale Rescue Rangers was planned but was never produced beyond a few voices. A quick clip of these voices can be heard in the Darkwing episode "Twitching Channels".
Darkwing Duck did have DuckTales' Gizmoduck as a recurring character. though.
And in one episode, the entire recurring villain cast from DuckTales showed up in one scene.
To the best of my knowledge The Powerpuff Girls have never crossed over with Dexter's Laboratory, but they apparently exist in the same universe (since Major Glory and several of the Justice Friends have appeared in both).
Eventually, this led to the Nicktoons Unite video game series, which had those three specials as their basis (and made some continuity nods towards them).
Seth Mac Farlane's Family Guy, American Dad!, and The Cleveland Show have had characters make occasional appearances, but the first true crossover among them is Night of the Hurricane, in which Hurricane Flozell affects all three shows and the actual "crossing over" occurs after the hurricane when Cleveland Brown, Stan Smith and Peter Griffin get involved in a stand-off.
Animaniacs sometimes did crossovers with other cartoons on its show, including one incident where Batman rescued them from an angry fairy (as Yakko's Shakespeare recital had foretold). Coincidentally, Batman: The Animated Series aired right afterward.
One Animaniacs episode featured internal crossovers, with Dot and Slappy Squirrel trading places, as well as shorts featuring Mindy and the Brain, Pinky and the Cat (Rita), and Pesto and Runt.
It was a bit more subtle than most of these examples, but G.I. Joe crossed over with The Transformers in the episode "Only Human". A masked character named "Old Snake" (voiced by Chris Latta) helps the Big Bad of the week with a machine to put Transformers' minds into synthetic human bodies. After the plan inevitably fails, Old Snake escapes and idly muses that "they just don't make terrorists like they used to", then raises his arms and yells "COBRAAAAAA!", ending in a coughing fit.
At the time the episode aired, it initially had a hard time fitting in with the events of G.I. Joe: The Movie, where Cobra Commander was transformed into an humanoid yellow cobra-man and then finally doomed to a fate as an actual non-anthropomorphic cobra. However in "Only Human", Cobra Commander is obviously humanoid and visible from his torn-up gloves are hands covered in yellow scales; presumably in reference to when he was transformed into a yellow-scaled snake man in the movie. Through what was likely coincidence, this seemingly erroneous depiction of a future Cobra Commander was later made to make sense: In 1989 (three years after "Only Human" originally aired), DiC produced a continuation of the G.I. Joe animated series, beginning with the five-part mini-series "Operation: Dragonfire". In this mini-series, Cobra Commander is still just a snake, but he's eventually returned into a humanoid form (specifically the snake-man form) by the Baroness.
And from the same season, recurring character Marissa Faireborne was obviously the daughter of Flint (Dashiell R. Faireborne) and Lady Jaye. The DVD commentary for Transformers: The Movie finally admitted this officially.
One "cameo" was made when a hologram version of an aged Flint was used in order to trick Marissa in one episode.
In a more meta case, all of Marvel/Sunbow's cartoons of The Eighties (Transformers, G.I. Joe, Inhumanoids, Jem etc.) were tied into each other via Hector Ramirez, an Expy of television reporter Geraldo Rivera. Hector would show up just about any time a story needed a television reporter, suggesting the shows all resided in a shared universe.
There was a multi-episode arc of Space Ghost where the title character went up against the Council of Doom, each of whom managed to defeat Space Ghost and banish him to some other realm/time/planet, just so the other Hanna-Barbera heroes of that setting could help save him. This allowed Space Ghost to team up with the Herculoids, Mightor, Shazzan, and Super Moby Dick.
The 1981/82 Hanna-Barbera show Space Stars was also built around this trope. Each hourlong episode would have a short eight- to 10-minute segment starring one of the show's hero teams: Space Ghost, The Herculoids, the Teen Force, and Astro from The Jetsons. The last five to 10 minutes of the show would then be a "Space Stars Finale" team-up between two or more of the groups against a common foe.
A later episode has a past incarnation of Johnny meeting Fred Flintstone.
The later seasons had a lot of episodes revolving around Johnny meeting other cartoon characters. Blue Falcon, Huckleberry Hound, "Weird Al" Yankovic...
Yogi Bear and Boo Boo once turned up in a Flintstones episode. Apparently, those bears are really, really old. Or able to time-travel. Or both.
A rare live-action to animation crossover took place on The Flintstones when Samantha and Darrin moved in next door (both series aired on ABC, and Bewitched was made by The Flintstones's (then) distributor Screen Gems). How old is Samantha, anyway?
And, as a bonus, Hanna-Barbera animated the opening titles for Bewitched and reused the characters designs for their stone-age counterparts.
Ironically averted with several of the later Flintstone shows, such as Fred and Barney Meet the Thing. They never actually met, it was just some Flintstone shorts mixed with shorts that featured a teenage version of the Thing.
Harvey Birdman, Attorney at Law is nearly built around this trope. Most episodes involved Harvey's law firm taking the case of some 1960s or 1970s Hanna-Barbera cartoon character.
He-Man and She-Ra did this more than once, as special episodes. Made sense, since they were siblings, but every time it happened it was a big deal. The two would do their transformation sequences simultaneously, making for a doubly psych-up scene. Strangelynote or not, if you're a cheap scene-recycling animation house though, despite being in the same place at the time, they would then each appear in front of their respective castles, which were located in different countries.
The show House of Mouse was all about Disney animated characters going to the house to watch various acts.
Buddy, the failed successor to Bosko, appeared in The Warners 65th Anniversary Special.
Bosko himself and his girlfriend, Honey were the subject of the Tiny Toon Adventures episode "Field of Honey" and let's not forget the lesser known characters of Foxy, Roxy, and Goopy being the focus of another
Which is wasn't unusual for Tiny Toons since the whole plot of the show is the main characters are the proteges of famous "Looney Tunes" characters.
[Homer and Bart accidentally pick up Bender of Futurama while driving through a portal tunnel]
Bender:Oh boy! You guys are gonna be my best friends, right?
Homer:You wish, loser!
[Throws Bender out the car.]
Then there was the time The Simpsons crossed over with The Critic, which Matt Groening was against since The Critic has a completely different style and therefore did not have Groening's involvement. Because of this, Groening's name is not shown in the credits for "A Star is Burns" (making it the only instance that this has happened). However, Jay Sherman made cameos in two other episodes that did have Groening's name in the credits.
And one of the show's couch gags featured the Simpsons meeting their Tracey Ullman Show counterparts sitting on the sofa.
The most recent Treehouse of Horror did this directly, with the Tracey Ullman Show counterparts appearing as ghosts. Furthermore, at the end of the segment, various versions of the Simpsons appear, including anime counterparts which parody One Piece, Bleach, Naruto, Attack on Titan, Pokémon, and Spirited Away. Other ones include Lego characters and Minions from Despicable Me.
Another couch gag had the Simpsons arrive on the couch via tubes right out of Futurama; Fry briefly appeared from a sixth tube before being sucked back in.
Interestingly, MAD did the very same crossover earlier.
Also the "Imaginationland" trilogy could also be considered something of a massive crossover as well.
Bart Simpson of The Simpsons appears in the two-part "Cartoon Wars". There are even references to his series, including mentioning that he stole the head off a statue once (a reference to the episode "The Telltale Head" and him saying "Cowabunga!" (in The Simpsons episode "Behind the Laughter", Bart, after a sketch written by Homer in which Bart has the line "Cowabunga!", remarks with irritation that he's never said "Cowabunga" in his life).
The Disney Junior preschool shows Special Agent Oso and Handy Manny had a crossover called "The Manny with the Golden Bear," in which Oso called in Handy Manny when he had to help a kid who had a broken bike.
Spider-Man: The Animated Series had a crossover with the 90's X-Men animated series. It was considered a big deal because it was a completely different animation studio involving the then current roster from X-Men in a show that was not their own. Even more impressive was the effort put in to keeping all the same cast (save for one, Gambit, presumably for contractual or scheduling reasons) for the sake of continuity. Even more fun, the crossover remains in continuity for Spider-Man, as Storm returns during the series' adaptation of the Secret Wars crossover event.
Robert Hays also reprised his role from Iron Man in several episodes.
The Marvel cartoons from around this era were frequently cameo-ing in each other's series, as well (though it's hard to know whether they were the same characters as the other cartoons; they all take place in aMarvel Universe, where a Spider-Man, Human Torch, etc. would likely exist somewhere.) You never know who'll be briefly shown watching from a rooftop, or looking up at the Pillar of Light in the distance when something really big goes down. Also, Iron Man, Fantastic Four, Incredible Hulk, etc. guest starred in each other's shows often enough to make the 90s Marvel cartoons a Diniverse of sorts - you can connect the dots through all of them.
The Venture Bros. started off as a parody of Jonny Quest. Eventually, characters from Jonny Quest started showing up on the show... or at least demented versions of them.
Victor & Hugo - Bunglers in Crime - Many times, either in reference or in guest stars. Count Duckula, Igor, Nanny, Hawkeye Soames and Dr. Potson (from Count Duckula), Danger Mouse, Colonel K, Baron Greenback, Nero and Stiletto (from Danger Mouse) and even a nod to Badger from 'Wind in the Willows. It seems fitting, since Victor & Hugo were a spin-off from Count Duckula, who in turn spun off from Danger Mouse.
An episode of The Zeta Project crossed over with Batman Beyond, justified in this case as the former was a spinoff of the latter. (Due to Bob Kane's contractual billing being what it is, this is also the only episode where the opening titles omit the "Created by Robert Goodman" credit - the end credits specify Kane's being behind Batman, with Goodman being behind the characters for the spinoff.)