Family Guyof all shows pulled one off in the episode "Brian Wallows and Peter's Swallows". First, Brian convinces a shut-in to enjoy the outside world, only to watch as she gets hit by a truck. They then spent her last few moments on Earth imagining what their future would have been like together with a virtual reality helmet. Meanwhile, Peter is forced to release some swallows who have taken up residence in his beard, and to whom he had gotten rather attached. Seth MacFarlane himself said this is one episode that contains "real emotional content".
In the otherwise hilarious "Road to Germany", the scene where nerdy Jewish Butt Monkey Mort Goldman, transported back in time to Warsaw in September of 1939, dances happily— the only moment of happiness we've ever seen the character have— with all of his old relatives at a wedding while "Tradition" from Fiddler on the Roof plays, interspersed with the Nazi invasion. It was as though the writers were acknowledging that even a Black Comedy like Family Guy has to address the Holocaust with at least one moment of solemnity before getting back to Those Wacky Nazis.
Brian's efforts to get people to realize animals' lives are as important as those of humans in Dog Gone ending in utter failure.
The scene pictured at the top occurs when, to prove that the Griffins love Brian, Stewie takes his collar to a bar and burns the bar down while a stray dog wearing the collar is inside. The firefighters are led to believe that the stray's burnt corpse was Brian thanks to the collar and give the news to the Griffins. Though the viewer knows that Brian is perfectly fine, it's still heart-wrenching to see the family's reactions.
There is also the episode when Brian plans to give up his kidneys to save Peter after Peter's kidneys shut down from drinking a homemade energy drink with kerosene in it. And when Stewie finds out, besides the way he cries, he feels pain because he believes Brian would leave him alone in the world. Plus the scene after Brian first agrees to give up his kidneys and Peter just hugs him tearfully, stroking him silently as Dr. Hartman and a tearful Lois look on.
The entire episode "Screams of Silence: The Story of Brenda Q.", but especially Quagmire's speech to his sister at the intervention.
"Brenda, the fact that you are being abused has affected my life in the following ways. The sister that I knew and loved growing up no longer exists. The person I see before me right now is just a punching bag. And I call you "person" and not "woman," because a woman is a strong, beautiful vibrant creature. A woman embraces life, a woman makes choices to make her life better. Sadly, the fact that you are with Jeff proves to me that you have made a choice to make your life worse. (tearing up) I...I want the girl who I grew up with back. I want...I...I want my sister back."
And this is coming from QUAGMIRE. The same Quagmire who often slips roofies into his date's drinks, steals women's used shoes to satisfy his foot fetish, has a sex doll of Lois hidden in his bedroom that he uses as a Stalker Shrine, and doesn't use protection at all during sex (despite that he has every venereal disease known to man) actually cares about his sister and wants her to get out of being abused by her boyfriend.
In "Amish Guy", Meg is told by an Amishman to stay away from his son. How does Meg respond? She actually cries. This even angers Peter!
Then near the end, when Meg and Eli share a final goodbye.
The episode where Peter gets a stroke and suffers just trying to live his life while his whole left side of his body is paralyzed. It was Peter's fault that he caused the stroke to himself by eating 30 hamburgers in one sitting, but for anyone who has or had a friend or family member suffering from a stroke, Peter's suffering can hit home.
Peter: I hate being all strokey!
The "Lieutenant Shiny Sides" cutaway in "Meet the Quagmires" is played for slight laughs, but it's enough to tug at the heartstrings of anybody who had a pet they really loved and were in denial when it died.
Peter:(pouring fish food into an overflowing fishbowl) Here you go, Lieutenant Shiny Sides. It's okay, you don't have to eat it now. You're just sleeping. You'll eat it later... You'll eat it later, Lieutenant Shiny Sides! (dissolves into Inelegant Blubbering)
In "Quagmire And Meg", nobody shows up to Megs 18th birthday party. It's sad because Peter and Lois actually feel sorry for her (even though the later episodes do show Peter and Lois as treating their children like crap — especially Meg, to the point that she may be mentally ill [a couple of episodes reveal that she cuts herself and hears voices in her head]). Lois even told Chris to pay kids from school to come.
Peter killing Quagmire's cat on "Episode 420" note The one where Brian petitions Quahog to legalize marijuana. The cat was one of the few things he loved other than women, and it's shown that he's clearly distraught about his disappearance (he didn't know that his cat was dead until the end when the main story about Brian's marijuana campaign fizzles out).
Quagmire: I'm raising the reward to 50 dollars for any information on James. No questions asked.
Some scenes from "Brian and Stewie," particularly the revelation that Brian keeps a gun and a bottle of Scotch in his bank vault for when the day comes that he becomes so sick of living that he can have one final drink before he kills himself, and Stewie telling Brian that he's the only person he cares about in this world and he'd be lost if he died.
Then Life of Brian came along, and for the short time where Brian is dead, Stewie really was lost.
Twelve-year-old Camilla Stull, who had fought a three-year battle with leukemia, had her dream of being an actress come true when Drew Barrymore introduced her to Seth MacFarlane and gave her a voice-over role in "Boys Do Cry". She died 13 days before it aired.
Basically, the treatment of Meg in the later episodes (in the early episodes, Meg was just a generic teenage girl character that wanted to be like the popular kids and hated her family for being embarrassing and not letting her do what the other kids do) is a major tear jerker. It's pretty depressing how the majority of the world hates you for just being yourself and treats you like crap. Dealing with physical and emotional abuse daily can really hurt your self-esteem and sanity, which is why Meg shows tendencies of mental illness.
Peter and Lois accidentally destroying Chris' self-esteem in "Space Cadet".
Also Chris writes an essay about what his teacher does after school, saying that she eats a roll of cookie dough, throws it up and puts doll clothes on a sonogram picture.
Actually, it's rather vague about whether it was a Imagine Spot or an actual flashback Brian was having. One thing was for sure: it went well with the song.
In A Fistful of Meg, after Meg was threatened to be murdered by Mental Mike in a fight, she goes to her mother for help. However, Lois coldly scoffs her for wanting to go to another school saying that it would cost too much, not noticing how she was clearly horrified for her life. Also in this episode, her own friends decided to steer clear of her leaving her alone to face her tormentor.
Let's not even start talking about "Life of Brian". By now, you've probably seen enough on the internet to know how much of an offender to this trope that episode is.
HOWEVER...all this it notably retconned Christmas Guy, in which Brian was saved from ever having been killed; since then, his death has been written out of the Family Guy continuity and has become much easier for fans to talk about.
The episode where Brian is brought back in question has Stewie asking for Santa to bring Brian back for Christmas, as this will be the Griffins' first Christmas without him.
Vinny's reaction to Stewie weeping for Brian, as he both feels sorry for Stewie and the fact that he'd never truly replace Brian. He even tries later on to emulate what Brian was like just to cheer Stewie up.
Also, despite their short time together, Stewie saying goodbye to Vinny before leaving to save Brian was pretty sweet.
From "Meg Stinks!"
Peter telling Meg that he does love her (despite all the crap and abuse she has to take from him) and doesn't wish that she was never born.
Peter crying when Meg tells him that she needs to grow up and go to college.
Really, the second half of "The Simpsons Guy" in general. I'd been looking forward to the "vs." aspect as much as anyone...but the first half? It really naturally felt like the two families were what each other had needed for a very long time.