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.
Freud Was Right: At least the fans like to think so. Arguably, many examples in game are indicative of this trope.
Good Bad Bugs: The boosted speed trick, which makes exploration a lot easier.
Goddamned Bats: Some of the Toriningen. They don't kill you (really, nothing in the game can except gravity) but if they hit you, they'll send you to a secluded area that you can either escape by waking up or by using the Medamaude effect which takes you back to the hub.
Stab something for a wonderful scream. An easy way to make this sound drive you insane is to take out the pointless room of walking eyes, or doing on of the few instances where you must stab a Toriningen.
It Was His Sled: How to make Uboa appear, as well as his very existence, which ruins a fair amount of the shock of discovering him. Then again, he has a 1 in 64 chance of appearing, meaning that most will never see Uboa anyway unless they either get very lucky or they explicitly try to find him. It can still be very shocking, however, when trying to find him, failing multiple times, doing it more just for the heck of it, and he suddenly appears.
Many of the named NPCs — specifically, Monoko and Poniko/Uboa(aaaaaAAAAAああああ) — have become just as popular as Madotsuki herself on certain Image Boards.
Within the fandom, "NASU IS VERY EXCITING!" and "Let's monochrome ourselves!"
Little do you know that Uboa actually has a smooth, English voice and enjoys long walks on the beach, that is after he sends you to an alternate dimension.
One that we can take credit for is pointing out that Uboa looks an awful lot like Che Guevara.
A drawing of Madotsuki vomiting has circulated around the web and received many spin-offs.
Ship-to-Ship Combat: If you don't ship Masada/Madotsuki, be prepared for a virtual shove-in-a-puddle. And the people who don't ship them are usually too busy shipping him with Shitai.
Tear Jerker: If you want to read some of the fan theories, I suggest getting a few tissues beforehand.
The teleporter maze as well. While it lacks in size, it makes up for with a confusing network of Teleporters and Transporters.
True Art Is Angsty: The reaction to the unofficial Alternate Endinghere. The general response is that it not only undermines the themes of the game, but also the ambiguity of its reality.
Monoko is what you get when you combine Body Horror with Moe.
Uboa, of all things, tends to get this treatment in fanart. It does have a big wide smile and eyes that suggests it's quite happy.
Western Gamers Love Yume Nikki: According to post No. 1420 on this page, Kikiyama was surprised to know that Yume Nikki was a lot more popular in the West than she expected.
Seccom Masada-sensei is often considered one as well, given where he resides: a spaceship in the middle of space, with no sentient company. If you take out your knife, he tries to get away from you. And then there is the table with two chairs, as if he would hope someone would come to him...
Mars-san, who's trapped alone in a cavern under Mars, looks as if it's crying, and its background music certainly doesn't help. It should be noted that it appears later on the same path as Secom Masada-sensei.