In-universe example - In Ed, Edd n Eddy, after the Eds wrongfully accuse Jonny of being a "serial toucher" and sentence him to rolling down a hill in a giant tire. When Double D calls Ed out on this, Eddy calmly responds "You know what they say, a little childhood trauma builds character." Given that The Movie reveals the abuse at the hands of his brother, Eddy might honestly believe it to be true.
The SpongeBob SquarePants episode "The Smoking Peanut" is about a clam at a zoo going berserk after SpongeBob throws a peanut at it. Several years later, a tiger escaped from its habitat and attacked three teenage boys at the San Francisco Zoo. Some people believe the boys had taunted it. Also in that same episode, the clam throws one of the zookeepers while on a rampage. In 2010, an orca killed one of its trainers at Seaworld.
Another SpongeBob one: In "Back to the Past", aired 2010, SpongeBob and Patrick ask Mermaid Man and Barnacle Boy in the altered present where they are workers at Man Ray's version of the Krusty Krab what happened to the younger Mermaid Man and Barnacle Boy (they had left the old, present ones with the younger ones back in time earlier). He explains that they are the younger ones, and that the older ones died and were buried in the very restaurant. The tombstones for Mermaid Man and Barnacle Boy are then shown, prompting SpongeBob to say "I am so sorry for your loss of...yourself." This became even moredepressing when the voice actor for Mermaid Man, Ernest Borgnine, died two years later on July 8, 2012.
In the Family Guy episode "Dog Gone", Brian unties a large dog left outside, only for said dog to violently attack and kill a smaller dog (before being shot to death by cops), this scene became even more uncomfortable to watch after something similar happened in real life. 
Also, the family crying after Stewie fakes Brian's death becomes this after Brian actually does die in "Life of Brian". Brian also gets hit by a car at the end of "Road to the Multiverse".
After "Joe's Revenge" anything related to making fun of Joe's handicap and his Hair-Trigger Temper because of his handicap becomes very depressing and awkward after it is revealed he was shot in the legs by a criminal, the story of how he was handicapped after fighting the Grinch was a fraud, and the episode was about him having his revenge after he escapes prison.
Peter's "Gary the No-Trash Cougar" character breaking into an elementary school cafeteria and threatening children with a gun in order to get them to throw out their garbage in the episode "Blind Ambition" definitely seems harsher as a result of the Sandy Hook Elementary School shootings in December 2012.
Three weeks after "Turban Cowboy" aired, the Boston Marathon Bombings happened. Suddenly, the main plot of Peter converting to Islam and being a pawn in a terrorist attack and the cutaway joke of Peter plowing through runners in his car aren't so funny (in a sick way) anymore. Even Seth MacFarlane called out having his episode being used in a video that "predicted" the bombings would happen. The episode was banned from airing on FOX and Hulu, but has come back on cable (TBS and Cartoon Network) and can be seen on Netflix's streaming program (of course, this was months after the Boston Marathon attack was news).
The infamous episode "Seahorse Seashell Party" angered many fans due to the Broken Aesop that "staying with your abusers is good for them", and the very next episode "Screams of Silence; The Story of Brenda Q." was a Very Special Episode that made it clear that staying with an abuser is bad. This led to many criticizing the show as being hypocritical or offering a hackneyed apology to those who offended.
The end of the episode "All Singing, All Dancing'' had Snake bothered by the family's constant singing and threatening them with a gun. To stop the end credits music he fires, just as Phil Hartman's name appears. Hartman would be shot to death by his wife months later.
Speaking of The Simpsons, it's a little unsettling watching the musical version of A Streetcar Named Desire where they call New Orleans "The Sodom and Gomorrah of the Mississipi" after Hurricane Katrina. Because of this, UK broadcaster Channel Four had to make a public apology for airing the episode around the time that news of Hurricane Katrina's destruction was still fresh in everyone's mind and it has become a Banned Episode.
With all of the original members of The Ramones now deceased, the scene in "Rosebud" where Mr. Burns orders Smithers to have them killed (although he mistakes them for The Rolling Stones) takes on a much darker tone.
Try watching "Bart of Darkness" where Bart thinks Flanders killed his wife now that Maude has been Killed Off for Real on the season 11 episode "Alone Again, Natura-Diddly". Or "Realty Bites" where Marge thinks the Flanders got killed in a house that was once the scene of a grisly murder involving a jockey and his wife. Or "The Springfield Connection," in which Homer tricks Flanders into thinking his wife and kids are dead by putting police tape outside his house.
The scene in "Lisa's Date with Density" where Milhouse ends up getting wheeled to the hospital after Nelson beat up Milhouse over a love note that supposedly was from him stops being funny thanks to the recent rash of gay, lesbian, bisexual and transsexual teens getting physically and emotionally abused in school (some of which have taken their own lives because of it). Particularly disturbing is the similarity to that scene's set-up to the murder of 15-year old Lawrence King by one of his classmates.
Many Simpsons episodes featured bullying as a comedic plot device — Harsher in Hindsight due to today's public awareness about the emotional harms of bullying, and several tragic cases where kids felt driven to suicide or violence due to constant bullying. If you're concerned over how cruel kids are these days, or if you were a victim of bullying, the following episodes won't be considered funny to you:
"Bart the General" — though at the end Bart warns that violence is never the answer
"Eeny Teeny Maya Moe" (the subplot about Maggie being bullied by babies and maybe the main plot about Moe cracking jokes about his girlfriend who is a female dwarf, but Moe does learn his lesson on not to be so shallow after Homer tells him that, despite what happened, he found someone who actually loved him and Homer does save his daughter from being bullied).
In "$pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling)," one of the many failures at Burns' casino is that Siegfried & Roy expies Gunther and Ernst are mauled by their own tiger while entertaining. Ten years later, it happened in real life to Roy Horn. The writers mentioned in the DVD commentary that the incident was bound to happen sooner or later and they were amazed when it did.
The beginning of the episode "Lisa vs. Malibu Stacy" note The episode where Lisa creates a doll that's actually a good role model for little girls while Grampa gets a job at Krusty Burger so he can be young and hip, only to learn that God wanted people to get old so they can criticize everything He's doing wrong where a bunch of elderly fans attack Matlock (Andy Griffith) and Grampa Simpson swipes his heart medication (and the subsequent shot of Andy Griffith getting rushed to the hospital) is now not so funny anymore thanks to Andy Griffith's real life death from a heart attack in July 2012.
During the cold open to the 2008 Halloween episode, Homer tries to vote for Obama, but the voting machine keeps repeatedly choosing Republican John McCain. Four years later many machines have been reported of doing the same supposedly in favor of both Obama and Mitt Romney (though this time because of poor calibration).
"A Totally Fun Thing That Bart Will Never Do Again" has Bart sabotaging a cruise ship so his dream vacation will never end, causing the ship's passengers to endure progressively worse conditions. In February 2013, the Carnival Triumph blew out its engines and was stranded for four days in the middle of the ocean before it was rescued.
"Sleeping with the Enemy" has Lisa being concerned about her weight and going to a store that sells ultra-thin clothing below size zero. This becomes even more painful after the CEO of Abercrombie & Fitch revealed that they don't make clothes higher than large because it discriminates against larger people.
In "Treehouse of Horror XII", at one point during the segment "Hex in the City", a helicopter crashes into Moe's Tavern, crushing Lenny and Carl to death. Then in 2013, it happened in real life when a helicopter crashed into The Clutha, a bar in Glasgow, killing ten people.
"Trash of the Titans": Viewed today (and ignoring the fact that this was the episode that had Homer as a full-blown jerkass), the episode seems like a satire about the rise of the Tea Party, as Homer goes around spewing angry rhetoric at a respected politician with little thought about how he'd do better if elected. Ray Patterson's lines "Nobody wants to hear the nonsensical ravings of a loudmouthed malcontent!" and "Simpson, the American people have never tolerated incompetence from its elected officials." hit harder than ever in light of how badly-received the Tea Party-dominated US Congress has been, receiving the lowest approval rating of all time in 2013.
In-universe example - In the South Park episode "Cartman Joins NAMBLA", the boys are playing "Investigative Reports With Bill Curtis," a Life-meets-Monopoly type board game in which players have to guess whether an event was denied or covered up by the U.S. government. When Kyle gives Cartman a jail-time card in the game, Cartman retaliates by giving him an AIDS card. The other characters are horrified by this. In the episode "Tonsil Trouble" (which aired eight years later), Cartman literally infects Kyle with AIDS thanks to a blood mishap.
The G.I. Joe episode titled "Cobra Quake" involves G.I. Joe trying to stop Cobra from causing an artificially created earthquake to destroy Tokyo. In 2011, an 9.0 magnitude earthquake actually hit Japan. Because of this, The Hub suspended airing this episode on its channel until further notice (though the 1980s G.I. Joe hasn't aired on the channel since the channel started putting on syndicated reruns of old family sitcoms and "Lois and Clark: The New Adventures of Superman").
In-universe example in the CatDog episode "CatDog 3001", where Cat taunted Winslow into exercising for a thousand years. Then CatDog were warped into the future in which an evil descendant of Winslow ruled Nearburg.