Welcome to the future, at least as seen through Futurama. Please be warned spoilers abound. Which makes sense, as this is the future.
The Dying Unit 44 in "The Six Million Dollar Mon".
"The Sting" may make you cringe forevermore at the sight of furry bumblebee bodies. Fry's death, Leela's hallucinations, followed by her descending into madness, her attempting suicide just so she can be with Fry, and Leela getting attacked by bees after she throws the honey against the wall. The only consoling thing is that none of this happened, Fry was alive, and that the whole thing was Leela's coma fantasy.
The space bees themselves. It's telling how dangerous they are when Professor Farnsworth, who's perfectly fine sending his crew on suicide missions, demands they not go.
This is because the Space Bees killed Farnsworth's old crew.
Seeing how Yandere the Planet Express Ship gets in "Love and Rocket" is actually rather terrifying, especially when she reveals she plans to kill Fry, Leela, & Bender to be with Bender forever.
"ME WANT ENGULF BENDER!"
Speaking of yanderes against Bender, the Don-bot's daughter Bella going after him while he's in the Witness Protection Program, wearing a mourning gown, armed with a laser gun and her bell making frightening church bell chimes And then it turns out that when she shot him dead, she killed a completely innocent robot and Bender was safe on Earth all along!
In ''Teenage Mutant Leela's Hurdles"', the crew all begin to age backwards and get younger and younger as time progresses. By the end of the episode, they're simply fetuses, and would suffer a Fate Worse Than Death... pre-life! Then death. They find a fountain of aging to get them back to their right ages, but Zoidberg unfortunately slips in, and he ages at such a rapid pace that he is dead by the time he reaches the center. Luckily, Turns out it wasn't Zoidberg, though. It was just one of his brothers that budded off, while there are miniature Zoidberg heads on a coral reef that they're all attached to. Seeing them all bicker does lighten the mood a little.
The end result of Bender being turned human in "Anthology of Interest II": he's not so much human- as blob-shaped and dies without anyone noticing. (Overlaps with Nausea Fuel- especially that bit where he pulls a sandwich out of his folds. Gaaah.)
People's life forces getting sucked out in "Thief of Baghead", and the fact that it happens so suddenly.
The Neptunian slug from My Three Suns. It looks harmless and kind of cute at first. But when Elzar takes it out of its cage afterward it starts growing rapidly in size with its teeth becoming sharp and menacing until it almost fills up the entire kitchen and looks as though its about to eat Elzar...
What happens when you dare break into Everybody Loves Hypnotoad with breaking news. ''No Hypnotoad! It's beyond my control! Don't make me kill myself!"
Zoidberg going on a hormone-fueled rampage through the gym in "Why Must I Be a Crustacean in Love?".
Instructor: Is there a doctor in the gym?
Zoidberg:I'M A DOCTOR.
Universe 25 from "The Farnsworth Parabox" especially this line. "We didn't see anything.......Ever!" 
"Murder on The Planet Express" has to be the creepiest episode in the whole series, it's a homage to The Thing (1982) with a shapeshifting alien creature that can disguise itself as any of of the crew and can swallow a person whole, which naturally leads to a lot of Paranoia Fuel, though it becomes Nightmare Retardant at the end when the alien is revealed to be a fake.
From The Beast with a Billion Backs, the tentacles' invasion, though partially Played for Laughs, is still rather unsettling. It takes up a lot of the movie, and the resistants are slowly dwindling, until only Leela is left. And even after Yivo is revealed to be a rather good, well, creature, you have to remember that skhler tentacles are actually, as Leela puts it, "gentacles". Everyone was horrified when they learned about it, which basically means that skhlee raped every living creature in the entire universe at once.
And then there's the throwaway gag that one family is responsible for evacuating all the waste of (apparently) everyone on Earth.
It could be a very large family...
From "The Six Million Dollar Mon", Roberto (a character who would be a good example of Nightmare Fuel to begin with) comes back from the grave when his brain is inserted into Hermes' robot body.
The scene where he rips off part of Hermes' skin so he can eat it (lucky for Hermes, Zoidberg didn't re-install his nerves).
In "Meanwhile", Fry jumps off the Vampire State Building believing Leela wouldn't come, only to realize far too late that his watch is minutes ahead due to his constant rewinding. What results is him constantly using the button to save himself, endlessly repeating the same near-death fall with no end in sight.
And it gets worse. The Professor distracts him, causing him to lose the button and he smashes onto the pavement, his bloody remains shown in all its glory. Luckily Leela uses the button, but its only enough to see him once again fall to his death. The worst thing about this? He remembers it all.
Proffessor Farnsworth being shredded to oblivion, though he does survive.
Finally, the idea that time has frozen for all eternity, while Fry and Leela live and age normally. If the Professor didn't arrive, or Fry threw away the remains of the button, it would've stayed that way.