New Brian, Brian's Mom, some random dog Brian ran over and Brian himself. Though a few episodes later he was saved by Stewie somehow seeing his past self and time traveled.
Meg is emotionally abused by her whole family throughout the show. Chris is targeted by a pe*ophile throughout the show. There are instances where Peter and Lois act violently towards their children.
There is frequent jokes about alcoholism, which Peter and Brian both definitely are, often Lois as well. There is jokes around addiction to smoking, energy drinks, meth, cocaine, ADHD medication.
There is constant jokes about se*ual as*ult and r*pe in the show. Especially with the character Quagmire who consistently jokes about drugging and r*ping women, amd sleeping with underage girls. The show mostly jokes about women being the victim, but there is also plenty of jokes and disturbing plots about men being the victims as well. There is an episode where Quagmire attempts to groom Meg for sex once she turned 18. There is an episode where Quagmire is arrested for statutory r*PE (although the girl slept with him "consensualy"), there is an episode where after a prostate exam Peter feels violated and reports to doctor for se*ual as*ult. There is an episode where Peter is sexually harrased by his boss Angela. There is an episode where Quagmire gets in a se*ually above relationship and it kidnapped and r*ped by his girlfriend. Consistently throughout the show Chris is targeted by their neighbor Herbert (an elderly man who is a pe*ophile.) There is a whole very disturbing episode when Meg is kidnapped and forced into s*x trafficking, Brian and Stewie save her at the end.
Yes. It is a running gag in the show that there is an old man in the neighborhood that is a pedophile. He is always chasing after boys (slowly because he has a walker), inviting boys over to his house, asking kids, to sit on his lap, etc. He is depicted as genuinely being a pedophile and for some reason it's supposed to be funny.
There are multiple references to Meg cutting herself, most notably in the crossover episode the Simpsons Guy, where she carved Lisa’s name into her arm.
In the episode "Petarded", Peter and Lois go to a restaurant. Peter rips a deep fryer out of the floor which results in Lois getting the deep frying oil all over herself and being burned alive.
There is a serial killer called the Fat Guy Strangler. He...strangles overweight men and tries to kill Peter. Several of his victims' bodies are shown.
In s13e05 "turkey guys" Peter hangs himself with the tie he receives for father's day.
In s12e03 "quagmire's quagmire", Stewie's previous teddy bear hangs himself in the end, right after Stewie takes Rupert back.
In s16e15 "woof of wall street" Rupert hangs himself during one of Stewie's monologues about Brian.
In the Season 4 episode “8 Simple Rules for Buying My Teenage Daughter, Peter, Stewie, Chris and Brian consume ipecac which leads to a prolonged vomiting scene
There's an episode where Peter and Lois believe "vaccines cause autism", but they are disproven by the end. In one episode, Peter "tests" whether his son Chris has autism by slamming cymbals behind his head. Much as I personally love this show, as someone with autism, I say Seth MacFarlane doesn't seem to know much about it. In a show like this, you can expect anything, and from time to time they will reference autism in a possibly disparaging way, so be careful of that.
In season 10 episode 2, Peter makes "dad noises" which many would considered grating. There's also an episode where he rubs a plastic wrap on a couch to make a very unpleasant sound that could cause pain in those sensitive to it.
SPOILERS included
Stewie develops multiple personalities after (the trauma of) walking in on his parents having sex. It's implied that the fact that he hasn't napped in days also caused it. Every time Stewie shakes his head another personality starts speaking. Brian convinces Stewie that his parents were just checking the thread count of the sheets, and within a couple of mins the other personalities are gone.
Few scenes where Peter is seen in a dress, and one episode where Peter is suffering from erectile dysfunction in which Dr. Hartman taunts Peter by being in a dress.
It's never explicitly said but it is implied that Peter said it to a bunch of black people in one episode and then he goes on to declare that they respected him for saying it.
"Fresh Heir" focuses on a father/son marriage (as a ploy to get inheritance that was given to the son, but sex and such between them is still referenced).
Some episodes feature bloody/gory scenes (heads ripped off / crushed, characters shot, etc.) mostly for comedic purposes. A few animals are killed in a brutal fashion throughout the show.