Are you talking about something like uncanny valley? (animation that looks almost human but not quite enough to be convincing and causes a sense of unease in the viewer) Because if you are I find animation styles like Strange Magic(UUUGH)s and Mars Needs Moms' to be really really unsettling to look at.

I don't know about cartoons per-say but I HATE drawing gore or seeing very gruesome gore (Entrails) in cartoons/anime, it's just absolutely disturbing X_X

Also the fear you're talking about is Kyrofelonoshophobia, its more common in children then others due to a cartoons odd look and a child's ability to make weird things terrifying.

GANTZ!! But the manga is an horror one so I doesn't count lol, also the alien duck from Courage the cowardly dog, but again it doesn't count lol.

I have never been afraid of an animation, maybe grossed out lol, but not afraid.

So when I saw Finding Dory in theaters, the uncanny valley and their shiny eyes sort of creeped me out. Everyone kept saying little Dory was cute but I thought she was the creepiest of all.

Also the reboot to Monster High
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I loved the original Monster High but this reboot...it just looks really creepy maybe because they look so dead behind the eyes.

@NickRowler
They want my soul, I know it!!
--runs away screaming--

I'm not afraid of any animaton style, but there are a few that I find a bit unsettling.

Uncanny Valley has been mentioned, and it can be very unsettling. It's worse in real life - with those creepy humanoid robots people are building (footage of those give me goosebumps) - but I find it difficult to be entirely comfortable watching 3D-animated humans that are very nearly realistic. Like, the Final Fantasy movies, or the Space Captain Harlock-movie. I spend a lot of the time with a small part of me feeling like something is wrong. Their eyes don't move quite right, their facial expressions change a bit too slowly, etc. - but on a still frame, they look human. It's weird.

I also am not fond of the animation style of things like Courage the Cowardly Dog, though that might be more of a holdover from my childhood dislike of the show itself - it, and several shows that were visually similar to it, were kind of loud and shrieky, and I was (and still am) fairly sound-sensitive when it comes to screeching noises, so I might be associating the two.

And as @NickRowler mentioned - the dead-eyed look is creepy! I find it's worse in 3D than in 2D, though.

Hahaha oh my gosh yes. The first time I watched Princess Mononoke and that boar burst out of the woods, I nearly choked on my tea. >.<

generic anime/manga, not real good anime/manga, just generic ones produced by random people who want to be the big mangakakaka they look up to. I see it all over comic sites and it's painful. I rarely ever follow manga comics because of this... most seem really uninspired and lazy.

Bad 3D. It's everywhere, so much so people think amateur 3D artists are just the norm. There's this trend with horrifying CG bimbos I see everywhere. Their lips look like gummy candy, clothes clipping into their flesh and their bodies made of Plasticine.

Characters with no noses and large mouths that take up the face. I've been seeing some SU/anime inspired artists take this approach and it is... horrifying.
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While I love Disney films like The Little Mermaid and Beauty And The Beast etc. the original Disney crew creep me out. Mickey Mouse, Minnie, Pluto, Donald Duck, Goofy, all of them. Creepy. I could never go to Disney Land.

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For some reason the cinematics in the old game Dark Earth scared the CRAP out of me when I was young and still kind of creep me out -

Though it wasn't even the violence that was scary to me, it was their FACES. Just....WHAT THE HECK IS WITH THEIR FACES?! Their overall movements are pretty disturbing, too.

So. I have one. Have any of you ever seen that show Almost Naked Animals? I saw it once. And the animals on it are so... like.. I don't even know. They're bald, but hairy and they have nipples and belly buttons and tan lines.. And I can't handle that show.

Man, I had a lot of those as a kid. And yet somehow I still kept watching them! I know everyone admires Ren & Stimpy for its animation/inventiveness, and as much as I respect it, I could never watch the damn thing. It was just too gross. I also had a thing about CatDog, there was this one ep about teeth that just drove me up the wall. Though, even cartoons I did like had a super-disturbing episode here and there.

As a kid I watched a lot of Russian cartoons and pretty much anything involving claymation/puppets was scaring me. They were just so....ugly. I just couldn't It's not until Chicken Run that I found out claymation doesn't have to be ugly and weird as hell.

there's a film called something like The Fantastic Planet with a really weird animation and art style, about big blue aliens. I physically cannot look at it without feeling incredibly nauseous... aside from that, I have a phobia of this like...particular kind of 3D animated floating orb kinda deal, it terrifies me.

Other than that i get easily squicked out by american gross-out cartoons like CN's golden age shows, those painted detailed close ups (a la spongebob) and any kind of art involving brains or eyestalks.

anything don bluth-style man. god it creeps me out something else

Realistic style done wrong. Or realistic cartoon style in general. It's neither realistic nor it's cartoon, the style gives me the creep.

Not really "afraid" but I can't stand super detailed "gross-out" shots some cartoons do, they always just make me cringe in disgust. Which... I guess is kind of the point? Never was into "grossout" humor.

The Yellow Submarine and its mixing of mediums kinda rubs me wrong, that and the creatures in it freaked me out as a kid

but i am getting curious to actually sit down and watch it

(never actually watched the movie, just commercial and the figure set terrified me as a kid, now its just creepy)

i think once your able to get over it's abstract art style it's a pretty enjoyable watch. I remember watching it on vhs with family as a little kid and even though the monsters were kind of creepy I thought it was pretty cool overall. If anything I think it's odd mixing of style was it's greatest selling point, aside from it featuring music by the Beatles, and was probably perfect having originally come out in i think the late 60s or 70s?

I think that like others have mentioned uncanny valley is the most unsettling. Then there's stuff like G-man from half life, and I've never once played the game but I've seen the one clip everyone seems to quote "Wake up mr. freeman"5 and anything that resembles that gives me the spooks. There's also Chulip, a video game yes, but between the graphics and probably the atmosphere of the game make it unnerving even if it has a "cute" appearance.

Y'all. If I ever see the Ren & Stimpy art style ever again I'm gonna cry acid tears. That is such a...ugh. No. Major no right there.

killing stalking grosses me out. couldn't even get past chapter two. I'm not sure why it appeals to some people but I just can't do it.
the worst part is that I ran into it by accident due to how much people were hyping it. Yuck
don't get me wrong, I respect the artist and her work is great. I mean, she's very talented to even create such grotesque work.

Clay-animation makes me uncomfortable most of the time. Other types of stop-motion I'm generally fine with, but clay... I don't like seeing it move.

Someone brought it up but I’ll hop on and say some forms of stop motion does mess with me. Rankin-Bass stuff, or even Gumby or Pengu is fine. But then there’s things like Jack Stauber’s work which just...

I barely made it three minutes into this before I hit fear goosebumps. (Which is sad because this seems like a good short )

Steven Universe is a fun show but some character designs from it (Spinel and Pink Diamond) unsettle me for some reason.

Jojo's Bizarre Adventure's style is definitely something i'm on the fence about. I like the anime version so far (I was on part 3 but got distracted) but the manga looks a bit uncanny valley.

H.R.Giger's art is something that I appreciate but am viscerally unsettled by to the point of not being able to look at it for long.

@Black_Conscious my brother showed it to me one day and it freaked me out lol. but then, it's always stuck in my head lol

I had came across this video and some of their other content and the vibe it gives off feels weird when you are beginning to watch it, and uh idk this isn't really somthin that's fearful but it is creepy, I guess if you put yourself inside the video than that's where I have to say I would be afraid.

(Some people had also said this was put onto YouTube Kids mistakenly, so sorry for you kids )

Edit: The name of their channel is also weird as well

I didn't think I'd have a response for but then I remembered something from my youth. When I was 8 or 7( a long time ago] I came across this image of the character Wolverine illustrated by Bill Seinkiewicz, In which the character had these huge hairy arms that were just so grotesque to me at the time. Now of course I love this image and Seinkiewicz is one of my all time favorites artists, but his work used to freak me out when I was younger. Lol

I'll take 2-D over CG animation any day.

2-D animation has an infinite range of styles even when it looks its ugliest. Most CG animation to me looks plastic no matter how often I see it.