These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Broken Base: There are many arguments between those who prefer the Japanese films over the American films and vice versa (although there are some who like both). Then there are those who believe the films to be inferior to the novels, etc.
Fridge Logic: In the American version. So...if Aiden knew helping Samara was exactly what NOT to do...why the heck did he keep it to himself until after the fact?
Fridge Horror: In the American version, Rachel finds out that one of the kids who watched the tape at the lodge died in a motorcycle crash, and she links it to the others' deaths by the time of the accident. The other victims were at home, surrounded by TV's and mirrors and such, so how did she get the kid on the bike? The inside of the visor on his helmet.
Genius Bonus (American movie version) - Who has even heard the expression "An appointment in Samarra", meaning inevitable death?
Hell Is That Noise: That horrible high-pitched screeching noise from Sadako's tape (this sound also plays during that phone call).
In addition, the high-pitched squeaks that rise in pitch when Sadako appears on Ryuji's TV screen.
From Ring 0: Birthday: the bone-crunching noises when Sadako's limbs twist and jerk during the climax.
The mysterious voice on Sadako's tape. It an only be heard clearly when the tape is played in slow motion, which makes it sound even creepier.
It Was His Sled: At one point in the distant past, the "twist" of the narrative (about how the curse actually works, and why giving Sadako/Samara a proper burial was pointless) and the "coming out of the TV" scene were shocking and surprising elements. Today, anyone who has heard of The Ring knows about the TV scene, which has become so iconic even this wiki illustrates its entry with it.
Magnificent Bastard: Ryuji, if the heavy implication that he's the mastermind behind Sadako's resurrection plan is to be believed.
Memetic Mutation: Apparently, when Moe collides with Sadako, Hilarity Ensues in many ways, from Pedobear hunting her to manifesting in disadvantageous situations (cell phone displays, for example).
Moral Event Horizon: The members of the theatre troupe in Ring 0 are extremely mean to Sadako right from the get-go, but pretty much all of the members cross the line when they corner a terrified Sadako and proceed to brutally murder her. When Sadako later comes back to life, thanks to being reunited with her evil half, she proceeds to kill them all in vengeance.
Meg's eternally smiling face in Terror's Realm, among other aspects of the game.
Nightmare Retardant: The look of the teenage girl's messed up face in the first American movie became instantly hilarious with the simple use of photoshopping phrases like "I like pancakes" on the wall. Also, some cute and/or funny fan-art of Samara exists.
Sequelitis: The Ring Two wasn't as well-received as the first remake.
The sight of Sadako's horribly rotted face at the climax of Ring 2 is arguably this when her lips start moving, but it still manages to be pretty creepy. Also somewhat justified, due to the film's low budget.
Squick: (Novels only) Watching the tape is bad enough normally. A woman watching it whilst ovulating gets a far worse fate, she is impregnated with a clone of Sadako who grows to full adulthood within a fortnight.
Uncanny Valley: The "Sadako Shuffle" —the halting, unnatural way she climbs out of the well and walks towards the screen— was accomplished by filming it backwards (likewise Samara's US version.) Then there are the chase scenes in both Ring 2 and The Ring Two, where Sadako and Samara are seen climbing up from the bottom with nightmarish speed and movement. In the American version, that vomiting thing on the videotape, as well as Samara's behavior that is recorded on the hospital footage.
The Woobie: Sadako. She doesn't seem like a Woobie to you? Just watch Ring 0.