Played with in A Bug's Life in form of the junior ants. First, they make a painting of the good warrior bugs and bad grasshoppers battling, and they painted one of the good guys dead because their teacher said it would be more realistic that way. Then, they perform a play of the battle, in which apparently, EVERYONE dies.
They started to show death in the Cars series films, from the gruesome end of Rod "Torque" Redline to the offscreen death of Doc Hudson.
Transformers: The Movie (1986) was famous principally for introducing this phenomenon to millions of Saturday-morning TV fans, when Optimus Prime dies, along with Megatron, Starscream, almost all the Autobots and an entire planet of Red Shirts in the first ten minutes, followed by the pointless on-screen maiming of several more robots including the last survivor of aforementioned planet for good measure, just to impress upon young'uns that Fiction Is Not Fair.
The animated series Exo Squad also used this trope, inspired by Macross and Robotech, quite daring for the time.
In the first episode of the second season, Terrorsaur and Scorponok fall in lava and die with relatively little fanfare.
Near the end of the season, Dinobot sacrifices himself with quite a bit more fanfare to save a tribe of proto-humans.
Tigertron and Airazor die, come back, and then almost immediately die again, this time for good.
Inferno and Quickstrike get toasted by their own boss. Depth Charge and Rampage go up in an immense explosion. Tarantulus gets hoisted by his own petard. And this is only counting deaths that lasted.
It's easier just to say that 22 characters were introduced (Including a fusion of two previous characters and a clone of another previous character) and that only eight of them survive to the end of the series (Optimus, Rattrap, Rhinox, Cheetor, Waspinator, Megatron, Blackarachnia and Silverbolt).
Beast Machines, the sequel series to Beast Wars, trims Rhinox, Megatron, and Optimus from the surviving eight. The death count of its new arrivals is harder to calculate; it depends on whether or not taking a character created by the extensive reprogramming of an old one and reverting him to factory settings counts as death. The new character definitely permanently ceases to be, but you may not consider that to be "dead." If it is counted, the death toll of Beast Machines new arrivals just tops 50%.
Transformers Animated was also pretty brutal. In the first season finale Megatron kills Starscream with the Allspark key, although he gets better a few episodes later. In the third season it got worse.
Blurr is crushed into a cube by Shockwave in Transwarped, Master Yoketron is left to die in Prowl's arms by Lockdown, Prowl sacrifices his life to stop the Lugnut Supremes from blowing up, and Starscream dies after the Allspark fragment keeping him alive is sucked out of his head. Since this was the final episode of the show, he probably didn't get better, though the comics show Blurr having survived.
There's also the sorta-deaths. Ultra Magnus is beaten nearly to death by Shockwave and we never do see him wake up from his coma (Word of God: Had they gotten a season four, Magnus would have bought it and Sentinel would have taken his place, and the dangerous acts he commits in his hubris would have only escalated.) and the Constructicons are blown up, with only Scrapper seen to survive. There's also the business with the gathering of the Allspark fragments. Since many of them had brought other Transformers to life and removing Starscream's fragment killed him, he may not have been the only casualty. Word of God says Wreck-Gar survived, but hasn't specified the fates of anyone else brought to life by an Allspark fragment. We're given hope in the fact that all the Allspark fragments were clearly not collected (Prowl's sacrifice was necessitated by the fact that not enough were gathered, and the reconstituted Allspark looks barely even half-complete, in fact - they left enough fragments out there to make the hoped-for comic continuation able to still use them as a plot point.)
The makers of Transformers Prime have said that "when we kill a character, we kill a character," and a few surprising deaths have happened. However, no main characters yet as of the season one finale.
Season two has Airachnid tearing Breakdown apart piece by piece. MECH then used parts of his body to build Nemesis Prime. He's Dead Jim.
And near the end of season two, Megatron blows a hole in Dreadwing's torso rather than let him kill Starscream. There's more hole than torso, and just like that, a fairly dynamic and important character is gone, and never mentioned again.
By the end of the series, this trope is downplayed. Out of all the Autobots that appeared in more than one episode, only two get killed off (if you include Zombie!Cliffjumper and his flashback episode). Out of all the Decepticons that appeared in more than one episode, only five get killed off (if you include Zombie!Skyquake, and if you believe that the Predacons mauled Starscream to death off-screen).
This is major gimmick of the Total Drama series. Well, technically, not die, but be elliminated, and can return to the show (and will - in the end of the season, to try to come into the next). Still, the number of active characters is rapidly decreasing and no one is safe, even the most popular and beloved by writers characters.
In a rarity for a children's programme, The Animals of Farthing Wood had a fairly high mortality rate, with a lot of the major characters being killed off as the series went on. By the end of the show only a few of the original animals still survived.
Frisky Dingo is one of the few [adult swim] original cartoons in which death is permanent, which it makes liberal use of by killing off both major and minor characters left and right during the second season.
Star Wars: The Clone Wars doesn't touch any of the characters from the films, but they are not afraid of introducing an original character and then kill them in the same episode. Jedi and well as clone troopers. Sometimes any original, named character surviving past an episode is a surprise. Sometimes.
Near the end of Season 3 they killed Even Piel, a back-ground Jedi master.
The entire message of Watership Down being "Small Furry Animals Will Eventually Die Anyway, so get used to it," so it includes all variants of on-screen cute rabbit death in order to drive home the message. It was felt that too many rabbits actually survived the book (Show, Don't Tell!) due to author's reluctance to pull the trigger. So additional doomed characters are introduced and a particularly sympathetic Woobie who played a big part in the novel is highlighted in order to be gruesomely Stuffed into the Fridge near the climax.
Vuk The Little Fox: The beginning of this children's cartoon seems to imply that it will be something cuddly and cute. Besides maintaining a level of cuteness, over a dozen characters (including those with names, personalities and spoken lines) die, either killed by other animals or by human hunters. There is no Carnivore Confusion, as the main hero kills and eats prey on-screen without any trouble.
The Venture Bros., after pointing on at great length in the "Lepidopterists" episode how 21 and 24's Genre Savvy made them indestructible, went on to brutally kill 24 in the season 3 final episode. His burning severed head lands right in 21's hands, making sure everyone knows he's dead for good.
And let's not forget the titular brothers themselves, who were killed at the end of Season 1. For awhile, this seemed to be final, until they got better when the second season finally started, two years later.
Since The Simpsons' Halloween episodes aren't part of the show's canon, the writers frequently end up killing off lots and lots of characters (not even the Simpsons themselves are safe.)
In Felidae, it doesn't matter if you're the Big Bad, The Dragon, a pregnant female or the most sympathetic character in the film. You're going down.
Chuck Jones spoofed opera in "What's Opera, Doc?". Saith Bugs Bunny, "What did you expect? A happy ending?" just before he died in Elmer Fudd's arms