Did Tamaki create the Host Club merely for the fun of it and in order to show off his good looks, or did he do it out of loneliness due to his background in order to gather "family members" he himself fancied, with the excuse of wanting to entertain ladies? Or maybe he did it for the others? He looked at the states of his colleague's lives (the family-pressured Kyoya, the antisocial twins, etc.) and decided that they needed the "club family atmosphere" more than he did.
Did Kyoya genuinely try to rape Haruhi, but was talked out of it, or was it just a test like Haruhi theorized?
Hikaru appears to get over his feelings for Haruhi really fast, going from nearly crying at the knowledge that he lost, to having no qualms about secretly following her and Tamaki on their date along with the rest of the club just a few days later. Though it might have been to symbolize how much he had grown and thus were capable of keeping his emotions in check, or he had been processing in getting over his feelings for a while.
In-universe: when Haruhi finds out about Tamaki's past she's impressed with how one wouldn't be able to tell by his attitude.
Awesome Music: Don't deny how cool the ending song is for a shoujo anime. The extended version used in the finale is even better.
Renge, who is either really funny or really annoying depending on who you talk to.
Haruhi. Fans will either find her apathy and snarkiness around shoujo males whom the heroine usually blushes around 24/7 to be refreshing and serving as a better "role model" for the average teenage viewer/reader, or make her bland and contributing little to the plot other than to be a generic snarker, and find her being an oblivious Dude Magnet for no other apparent reason but that she's "cute!!!" to be obnoxious. It also got turned around later in the manga when she realized that she'd fallen for Tamaki: fans who didn't find her smitten attitude around him to be hilarious believed that she had turned into exactly the stereotypical heroine they had loved her for not being. Even as she more or less returned to her old self after calming down from her initial reaction, it still didn't keep the fans who had expected her to be a unique heroine who didn't have to end up with the male protagonist from leaving and never coming back.
Tamaki is debatably the most popular character in the series, but there are also those who just find him annoying.
Honey is another incredibly popular character, but there are also those that find an 18-year old acting like a 5-year old to just be creepy.
In one episode there's a scene where the twins are lying in bed in front of their maids. One of them pulls off the covers and reveals he's wearing a colorful elephant head on his crotch, that blasts confetti into the air. This is not given any lines, and it goes onto the next scene quickly afterwards, with this never being explained or mentioned again, except for a brief moment that implies that they plan on doing it again. (The elephant head is a common way to censor out nudity, so that's probably what that was.)
The twins being randomly dressed as girls at a party during their childhood, though only in the anime. (In the manga, it's established that their mother had designed a children's clothes line at the time, for which she used the twins as models.)
Bizarro Episode: There was the random episode that was a parody of Alice's Adventures in Wonderland featuring random single-episode characters from throughout the first season showing up again... In the anime, the end is a Tear Jerker: the whole thing is a dream of Haruhi's, and the one playing the Queen of Hearts is actually her Missing Mom Kotoko.
Haruhi's father's friend Misuzu is extremely popular, the few times he does appear.
Fanon Discontinuity: Many people, especially in the West (and especially nonbinary and trans people), ignore the episode where the boys keep insisting Haruhi is a fragile girl who should realize that. While the message of being cautious isn't something to laugh about, the way it's executed oozes with Unfortunate Implications, and to top it all off, it's the episode where Kyouya pins Haruhi down to make sure she "realizes" that she shouldn't trust so easily, and there's still enough ambiguity left after Haruhi's theory that leaves people questioning Alternative Character Interpretation above. All in all, for a good deal of people, the episode didn't happen.
Girl Show Ghetto: Averted. Despite being aimed at a female audience, many guys enjoyed watching the show, mostly because of the light-hearted humor and the constant self-parody of Shoujo clichés.
Growing the Beard: The series starts out as mostly a comedy and (as mentioned above) Affectionate Parody of the standard shoujo clichès, with the occasional yet brief serious or heartwarming moments, but becomes deeper and more serious the longer it goes on, revealing hidden depths within many of the Host Club members along with other characters such as their families, and testing of how strong their bonds truly are (specially in the manga, though some of it in the anime too).
Harsher in Hindsight: An in-universe example: in Episode 14 of the anime, Akira Komatsuzawa, the newspaper president, becomes obsessed with the thought that Tamaki can't be such a perfect Nice Guy as he appears to be, and there must be something evil or scandal-like to him, or even if there isn't, he'll make something up. In the end he's thwarted by the rest of the Host Club, and Haruhi's left with her doubts that there would be anything bad to find about Tamaki. Come the last two episodes of the anime (or Chapters 25-26 of the manga) she (and the audience) learns how Tamaki does have a sad and scandal-worthy past. The short version is that he's a mistress' child, and he's forbidden from seeing his mother ever again by his Evil Matriarch grandmother. Towards the end of the manga however, it turns out that their customers knew about this, due to always wanting to check out the background of their favorite hosts, and because of Tamaki's kind and cheerful self they were fine with it.
That episode where a boy thought Haruhi was a cross-dresser. Then we meet her father.
The creator early on in the series said she couldn't see Haruhi getting together with Tamaki. Guess how it ends.
Maaya Sakamoto (Haruhi) and Kenichi Suzumura (Hikaru in the anime and Kaoru in the drama CD) (as of August 2011) got married. This way, the Hitachiin twins/Haruhi OT3became real.
Kyouya is nicknamed "The Demon King" due to his sinister nature. One of J. Michael Tatum's more well-known and famous roles is Sebastian.
Haruhi is an awful actor and her music grades are apparently no better. Her Japanese voice actress is a famous singer. Fun fact: The voice Haruhi was lip-syncing to in episode 19 was actually her voice.
The fact that Haruhi falling for Tamaki can be applied to Truth in Television: some studies will suggest that people have a tendency to unknowingly fall for someone reminding them of their parents due to the comfort of familiarity.
Incest Yay Shipping: Hikaru/Kaoru of course, being a heavily invoked in-universe example and probably among the most famous anime examples out there. Even people who don't care for incest shipping often give them a pass as it's mainly Played for Laughs.
It Was His Sled: The fandom doesn't keep secret that Haruhi ends up with Tamaki.
Kyoya also seems to be a popular ship magnet, getting paired with Tamaki, Haruhi and Kaoru.
LGBT Fanbase: Nonbinary people are fond of Haruhi, and with how she/they often say gender doesn't matter, and even early on expresses "Biologically speaking, yeah." about being female, Haruhi is considered so as well.
Tamaki's scolding of Haruhi for trying to protect customers from a pair of drunkards, which seemed to boil down to "Girls are too weak to fight boys!" rather than "A small person shouldn't take on two brutes." Although, the Host Club points out that their main concern was her attempt at taking them on alone when she could have called for help, which needlessly put her in danger, and she really had no fighting skills to begin with anyway.
There's Kyoya's famous threat of rape of Haruhi later the same episode, which is quickly shrugged off by the characters and narrative in whole, being treated as acceptable because he was "pretending in order to teach her a lesson" and Haruhi, at the very least, doesn't believe he has any intention of following through.
Western fans have a harder time swallowing the obsession with characters like Honey or Shiro, whose admirers specifically like that they appear to be, or actually are, a pre-pubescent child and act like one.