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.
YMMV: Bakemonogatari
Nightmare Fuel: See No-Holds-Barred Beatdown on the main page; Suruga's constant hysterical screaming of "HATE HATE HATE HATE HATE HATE!!!" while savagely beating Koyomi is quite disturbing.
Crosses the Line Twice: Koyomi getting into a fight with a 5th-grader, beating her up (mildly), and then laughing about it. The fact that she's already dead may or may not make this worse.
Crowning Moment of Heartwarming: Episode 12 basically, especially the last few minutes. Nice things happen for a change in an otherwise screwed up world.
Crowning Music of Awesome: "Prologue", the track that plays over the "Kizumonogatari" montage in the beginning. Check it out on a Haruhi AMV here. It's badass.
The violin piece that plays while Koyomi bathes in Nisemonogatari is rather interesting.
The piece with the bells near the end with Shinobu.
Ensemble Darkhorse: Shinobu: Fifth place on the popularity polls while not speaking a single word and getting relatively little screen time is pretty impressive.
Nadeko: Recent character popularity polls has confirmed that she is currently the most popular character of this show, despite her arc is the shortest among other sub-heroines.
Everyone Is Jesus in Purgatory: Fans have theorized that all the oddities simply stand in for otherwise mundane life problems; the ones with the most merit are Hitagi's (her "weightlessness" being caused by an eating disorder) and Suruga's (well, extreme jealousy. There's barely a stretch there).
Fan Nickname: Ararararararagi-san. Attributed to Mayoi's frequent mispronunciation of Koyomi's name. See Running Gag on the main page..
Fashion Victim Villain: Deishuu Kaiki. A tie you could jump rope with, that one. And that dress shirt is damn near an actual dress.
Fetish Retardant: When the Meddlesome Cat grabs Koyomi from behind, he licks his neck in a very sensual way. What's the problem? That the Cat's tongue is sharp enough to open Koyomi's carotid artery.
Harsher in Hindsight: When Tsubasa finds Koyomi beating up Mayoi, she tells him that it's wrong to hit a child without telling them a justifiable reason. We later find out that Tsubasa's stepfather physically abuses her. It's likely a deliberate example; Tsubasa has Scary Shiny Glasses as she makes the former statement.
Internet Backdraft: Thanks to an anonymous user now called "Gorespammer" relentlessly trolling and reverse-trolling the series, it's pretty much impossible to have a serious discussion about it on /a/.
Magnificent Bastard: As said by Koyomi in Episode 8 referring to Oshino: "You... Even compared to a devil, you're such a magnificent bastard."
The Masochism Tango: Araragi and Senjougahara aka Crazy Tsundere Stapler Girl's relationship is about as weird and unlikely, and usually downright sadistic as it gets. And yet somehow it works, for them.
Moe: Well, yeah. Though not really a harem anime, it has one guy and a bunch of girls, all of whom fall into traditional moe characterizations. In fact, some of the more Genre Savvy characters make fun of it, like Oshino's habit of calling Senjogahara Tsundere.
Rescue Romance: Shortly after regaining her weight, Hitagi declares her love for Araragi. It's somewhat subverted in how she believed that even if he didn't help her, she would've fallen for him anyway if she simply observed him rescuing others.
Though in Nisemonogatari she comments how she might have fallen in love with anyone who rescued her, and feels extremely frustrated by this fact.
Tear Jerker - The last episode. When Araragi realizes that when Oshino told him "I'm going to leave this city one day", that in fact was his way of saying goodbye, because he doesn't like formally saying goodbye. Whilst we already know Oshino is a Jerk with a Heart of Gold, this shows that he is incredibly soft when it comes to goodbyes.
Unfortunate Implications/Fan Disservice: The overall sexualization of Nadeko (as well as the bizarre treatment Araragi gives to Mayoi) trend in an unfortunate direction.