Some of the best examples include the air conditioner's blow out (and his dead corpse sitting in the dark in the back of the room for the majority of the film afterward), Toaster's nightmare, the deeply unnerving and upsetting flower scene, the various Family Unfriendly Deaths, etc.
A literal Fridge Horror moment: When the appliances decide to leave the house they try various methods of travelling, including Kirby pulling them along in a fridge. Later on in the film we see a fridge that's alive like the the appliances. But the one in the house wasn't animated at all...the appliances were literally riding on the corpse of a dead fridge!
Borderlining on Fridge Horror as well; when one closely observes the movie after childhood, it will become frighteningly noticeable how many suicides/attempted suicides there are in it - Kirby swallowing his cord; the Air Conditioner making himself blow out; Lampy almost killing himself via electrocution; the one green car willingly driving onto the rack heading for the crusher; the flower losing all will to live and shows strong implication to not survive long past its scene; and of course Toaster sacrificing himself to save his Master.
Think about the Air Conditioner for a moment. This is a character that is wedged in a wall, and has spent his entire life watching as the kid (or rather, The Master) would play and interact with the other appliances. His 'function' was just to sit there and watch something he couldn't have. He flat-out STATES this as he short-circuits in a scene that can easily be seen as a bitter man committing suicide in a fit of rage.
The scene where Blanky is lost in the dark, stormy forest all night, and then the battery is going out, and even though the battery gets recharged, we are led to believe that Lampy died in the process of said recharging! (Though granted, we are able to breathe sighs of relief, when it's revealed that he survived, apart from a broken bulb and a cough.)
Lampy being struck by lightning. It shouldn't happen to such a nice cartoon character!
The worst part is when a blender is dismembered by the goofy shopkeeper who laughs as he does it. This is played exactly as if it's getting brutally murdered (which on the level the audience is watching it really is), dripping fluids and all.
"It's a B-Movie". Menacing, deformed appliances, the little plaintive part in the middle ("There goes the sun"), and the spooky shadow puppets. Heck, there's even an Eye Scream with the portable fan thing.
The lyrics are downright creepy as well:
"There goes the sun Here comes the night Somebody turn on the light Somebody tell me that fate has been kind You can't go out you are out of your mind!
The oven basically eats and vomits the main characters in the middle of the song.
The Mish-Mash◊, which has been driven insane by the deformed and mutilated condition she's in.
Look at me, I mean, really! Barf, barf, barf. I'm a can opener, a lamp, and a shaver. Oh god, I'm a mish-mash!
She then flops down, either unconscious or dead, and gets lifted away by a bunch of cords.
The magnet. Oh, God, the magnet.
An angry creature from above chasing you wherever you hide? And you CAN'T MOVE? 100% Paranoia Fuel.
Making this scene even worse is when you really get into the idea of a "Junkyard". In this movie, it becomes a disturbingly grotesque mass grave...
How about Rob's near-demise? Seeing the cars get crushed one by one is bad enough, but when a human is there, someone we can physically relate to, that's even worse!
The worst part about that whole magnet scene was the fact that even when he's picking up cars, the magnet has eyes (if hostile, glaring ones) that humanizes it. However, when it crosses the line into actively homicidal in trying to kill Rob, its eyes disappear, erasing any humanity in it and rendering it more frighteningly alien.
The song "Worthless" is packed full of Nightmare Fuel that would probably only apply to older people watching the film, since the catchy but fairly complex (for a kids' movie) lyrics are riddled with oblique hints of aging, death, and suicide. Seriously, try imagining humans singing that song and see where your mind takes you.
The compactor is more-or-less eating the cars.
This line may be the most chilling in the entire song, and that's saying quite a lot:
I took a man to a graveyard I beg your pardon, it's quite hard enough Just living with the stuff I have learned.
This can hit kind of hard to anyone who has had depression:
I just can't I just can't I just can't seem to get started Don't have the heart To live in the fast lane All that has past and gone.
The car that sings about how she once took a Texan to a wedding. The lyrics state that 'he kept forgetting, his loneliness letting his thoughts turn to home and we turned' revealing that they crashed on the way to the wedding. This is immediately followed by a car declaring that he took a man to a graveyard ending with those two cars going into the compactor together. It's not hard to believe that the Texan who crashed on his way to the wedding was the same man who got taken to the graveyard.
And don't forget the one car who, after singing part of his verse about how his life has amounted to nothing, jumps onto the conveyor belt of his own volition. The people who wrote this must have been going through some seriously tough times. Supposedly, the writers intended to show that car sacrificing itself for another vehicle, but it ended up looking like a suicidal move.