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.
A British English exclusive example from the Disappearance: "His spunk was nice and all"
And from the movie:
Kyon: I haven't even tasted Haruhi's hot pot yet.
Adaptation Displacement: Wait, there are books? And there is a small group of fans who, upon discovering the novels, immediately think that the books are adapted from the anime and manga material, as opposed to the other way around. Head, meet wall. Become good friends.
Good Lord. It would be faster to list characters who don't have followings with widely varied opinions. Not even Those Two Guys are immune. Has its own subpage.
Deliberately fueled by the author himself. Itsuki hints that both he and Mikuru are merely putting up acts in order to fit the personalities that Haruhi expects them to have. However, neither the show nor the novels have actually shown this to be true.
Author's Saving Throw: Though planned before base-breaking "Endless Eight" and character re-visualization in the anime, both producers and fans hoped the movie would be this. It succeeded.
Haruhi... to the fanbase of a series where she's the titular character!
Kyon doesn't reach Haruhi's level, but he's either the most original and generally awesome Lemony Narrator or a pedant who really needs to shut the hell up.
Better on DVD: Endless Eight, assuming you're an American fan who can buy a boxset instead of having to pay the ludicrous prices for multiple DVDs of the same damn thing. Downing the whole thing straight may take four hours of your life, but it actually does hold up as an experiment. Failing that, it's at least better than having to watch the same damn episode eight weeks in a row.
Broken Base: Endless Eight. To summarize each side's arguments: those for "Endless Eight" argue that the episodes are distinct because each is animated from scratch, and call it an incredibly effective illustration — if going through the loop eight times is grating on your nerves, imagine how Yuki feels). Those against "Endless Eight" call it meaningless filler with virtually-identical scripts that wasted almost an entire season on what was a single, brief story in the novels. And then, there are those who think that it was a waste of animation, but the fan meltdown was more hilarious than anything Kyo Ani could have animated, so it was worth it after all. The franchise, especially animated, has never been afraid to screw with viewer expectations so it was pretty much in keeping with the nature of the show. It's been compared to Monty Python's Flying Circus for a reason, after all.
Some Yuki/Kyon and Mikuru/Kyon shippers really hate Haruhi and will cheerfully Demonize her. Played with more literally in the series itself — if Kyon is too nice to Mikuru, Haruhi gets jealous and (unbeknownst to herself) uses her powers to rewrite reality.
Yuki and Mikuru get a bit of this as well. Apparently, it's due to backlash for Haruhi being Out of Focus in the last novels.
Some of the other songs (like God Knows, and the character songs) may qualify for this as well.
In-universe example in the Drama CD "Sound Around", which later manifests as an actual worm-like monster. The end of "Sound Around" implies that Hare Hare Yukai is so popular because Haruhi composed it with this trope in mind.
The episode that wouldn't die, "Endless Eight". The visual style of each iteration came to reflect, and subsequently reinforce in viewers, the fatigue experienced by Nagato.
The Disappearance of Haruhi Suzumiya for some people, it goes on even after the resolution and it's almost three hours long. Though the fact that the epilogue contains one of Kyon's biggest CMOAs in the series helps offset this.
Ensemble Dark Horse: Taniguchi, Tsuruya (and her superdeformed version, Churuya), Ryoko Asakura, and to a lesser degree Emiri.
Epileptic Trees: Lots of this in the fandom. But considering how often the animators screw around with the audience just for the sake of screwing around with the audience, it's understandable. This is made ten times worse by the fact that many very important plot points have been hinted at or foreshadowed in seemingly-innocuous small talk and apparently tangential commentary. This has, of course, led to people combing over every single bit of text and conversation to try and figure what is going on.
Haruhi, at the beginning. Evil in that she is willing to blackmail a computer club president through false incrimination. Sexy when it comes to her appearance AND her Genki Girl personality.
Also, Ryoko Asakura and every member of the "Anti-SOS Brigade".
Family-Unfriendly Aesop: If someone steals your computer using false blackmail, you have no right to be angry about it. It's okay for Haruhi to use an underhanded tactic, but the Computer Club are bastards for attempting to cheat.
"In fact, if you really wanna get technical and bring Haruhi into this awful awful event that's destroyed and displaced the lives of Japan's citizens, I bet you anything it was Haruhi's "friends" who caused this earthquake in order to give the loopy cunt something to be fixated on to prevent her from destroying the universe in one of her many bitch-fits bought on by her own narcissistic personality disorder."
Haruhi is God. Most fans of the anime took Koizumi's speech in the 3rd chronological episode at face value, but other scenes in the novels and the anime (especially the 2009 version) cast doubt on it:
In the third chronological episode, when Koizumi tells Kyon that Haruhi is God, he presents it as the belief of the "higher-ups" in his Agency, and acknowledges that various people in the Agency have different ideas about how to deal with Haruhi. He also describes the theory as the "worst case scenario" that his Agency is acting to counter, which suggests that they're playing a form of Pascal's Wager: even if they're not certain whether Haruhi is God, they think it's just likely and dangerous enough that it's better not to risk the consequences of neglecting to placate her.
In the Sigh novel and anime, Asahina tells Kyon to be skeptical of Koizumi and his Agency's theories, and that the time travellers disagree with them. Nagato speculates on the time travelers' theories and their incompatibility with the espers', and hints that the Data Overmind believes something yet different about Haruhi. And to top it off, Koizumi himself also contradicts his earlier explanation that Haruhi is God, theorizing instead that Haruhi must be somebody chosen by God to fix the world.
In novel 9 we run into a whole three new factions, at least one of which (Kyoko Tachibana's espers) clearly disagrees with the assertion that Haruhi is God. Or at least she says they do.
There is a camp that believes Kyon is really the god-like being playing his (conscious and unconcious) fantasies out through Haruhi. Can anyone say "Freud must be laughing at me right now?"
Did you know that the mathematical, physical and chemical formulas seen in the opening animation (Bouken Desho Desho) are positronium, Lambda baryons, benzene ring, cyclohexanes, infinite number, Titius-Bode law, Planck's constant, Drake equation, time-dependent Schrödinger equation, Hubble's law, infinite product, definition of information entropy, large numbers, stationary Schrödinger equation, the theory of relativity, probability axioms, definition of Laplace operator, the wave equation in one space dimension, and small numbers? (source: http://seinenramen.wordpress.com/2006/12/05/physicsmaths-in-suzumiya-haruhi/ ) Also, this wasn't just pulled out of a physics books, the writer Nagaru Tanigawa loves this stuff.
The novels have even more, with countless throwaway references to astrophysics and at least one in-depth discussion (and illustrations) of Euler's planar graph formula. And let's not even start about the time travel incidents that reach a complexity where you just want to overlook it. Koizumi even talks about time-lines and alternate realities at the SAME TIME,with some explanatory VISUALS.
Also, Dissociation mentions Yuki reading a book about "Mathematicians, Artists, Musicians, and their Interrelations". This is probably "Gödel, Escher, Bach, an Eternal Golden Braid.", by Douglas Hofstadter. The book deals heavily with recursion, parallel worlds, and uncertainty. Suspiciously Apropos Literature or what?
Some careful observation reveals a bit of philosophy thrown in, although I'm not sure why Kyon ascribes to Albert Camus' way of thinking.
The rapid-fire speech capabilities of Yuki Nagato and Ryoko Asakura are actually human speech sped up 400%-500% and reversed. A few interesting things arose after decoding:
Yuki appears to be speaking in SQL.
Asakura asks Yuki, during their fight: "You love Kyon-kun, don't you? I know you have realized it."
Itsuki sometimes stands a little too close to Kyon for Kyon's peace of mind. Also, he is the only male path option in the visual novel The Perplexity of Haruhi Suzumiya.
Of course, there's Haruhi being all over Mikuru. And Yuki and Asakura, especially in Disappearance and in the way Asakura speaks of Yuki in the first part of Surprise.
A less one-sided example would be Yuki and Mikuru, which is particularly noticeable in "Remote Island Syndrome" and even moreso in Scheme.
We then have Kyoko and Sasaki, what with Kyoko's worshipful attitude toward her, and Sasaki and Haruhi, what with Sasaki's worshipful attitude toward her.
Internet Backdraft: The second anime season also attracted quite a bit of criticism because it seemed like Kyo Ani was wasting everyone's time, effort, and money by simply recycling the same script but with completely redone animation and voice acting each time.
Jerk Sue: Haruhi at the start of the series. This is invoked because the plot-line literally revolves around her.
According to fans, Mikuru's Eye Beam attack is one of the most destructive forces in existence. Considering how many different variants on the "Mikuru Beam" ended up coming out of her eye (and eventually sealed away by Yuki), this is entirely possible.
Kyon's getting there himself, as exemplified at the end of Disappearance when he leads Yuki and Mikuru back in time to save his own life and ensure the return of their recognizable world. They may have weird powers, Haruhi may attract weirdness, but Kyon can MOBILIZE it.
Yuki's endearing lack of understanding towards Earth society, coupled with her quiet, innocent personality and her hidden kindness makes most people want to smother her with a big-giant-hug. Her small and cuddly appearance only serves to make her even more adorable. In fact, Yuki even made the Top 8 during Saimoe 2006, directly defeating both Mikuru and Haruhi.
Yuki in Disappearance is this trope cranked up to 11. Seriously, it has to be seen to be believed. This is acknowledged by Kyon in the novel. He thinks that Yuki is ridiculously cute when she starts blushing and fidgeting.
Ryoko does have a pretty cute smile and a nice figure. Because of this, she has quite a few fans, both in-universe (Taniguchi rates her as an "AA+ " on his good looking girls scale) and out (despite the knife tendencies).
Mikuru. She's called moe in-series for crying out loud!
Either Kuyo's attempt on Kyon's life in Vol. 1, or crucifying Haruhi in mid-air on Fujiwara's orders in Vol. 2 pushed her over, but it's quite obvious she crossed it somewhere in Surprise if she hadn't already by debilitating Yuki in Dissociation.
Attempted deicide pushed Fujiwara over the line at the climax of Surprise Vol. 2.
Haruhi herself either subverts or inverts this in Sigh when she and Tsuruya spike Mikuru's drink (definitely a subversion in Tsuruya's case by virtue of her holding the Idiot Ball as usual). After Haruhi nearly gets a faceful of fist from Kyon for the effort (it didn't help that she went so far as to call Mikuru ''her toy''), she pulls a Heel-Face Turn and from then on is both a Type II Anti-Hero and a Jerk with a Heart of Gold.
Never Live It Down: Haruhi will never be able to get away from the reputation she established in the beginning; even if she gets Character Development from it, some fans will inevitably continue to see her as an irredeemable sociopath that never defrosts. Although, to be fair, most of the material in which she does defrost had not (and still has not) been animated yet, and the novels are still pretty niche in the Americas.
You were almost forced to it in the first airing, due to the Mind Screw episode order. However, even in the chronological order, there's an enormous amount of bonus.
Also, although you can skip the middle episodes of the Endless Eight and only watch the first and last ones the ending of the final episode is much more satisfying after having endured the whole thing. Not to mention each episode has subtle changes that are hard to catch the first time.
The Scrappy: Haruhi to some, due to her incredibly dickish behavior at the beginning of the series. It's worth noting that the people who don't like the series more often than not cite her as being their main turn-off towards the series.
After Haruhi, the character you'll find the most criticism is Mikuru. She's seen as useless and annoying, and held up as a shining example of the "moeblob" type of character who's only there to look cute and provide fanservice. Her character is probably one of the most common complaints you'll hear about the series, even for fans.
Seasonal Rot: The second season was not as well received as the first season or the movie, largely due to Base Breaker "Endless Eight."
They Changed It, Now It Sucks: Many fans reacted this way to the new opening and ending sequences created for the 2009 episodes. Admittedly, the old themes had three full years to become ingrained into the collective fan-consciousness, and the ending theme especially achieved godlike levels of popularity, spawning thousands of fan-made videos and animations. Fortunately the creators of the anime were seemingly aware that they could never top themselves, and avoided the temptation to try simply by coming up with something Completely Different (neither of the new themes feature any dancing whatsoever, and their visual styles are quite distinct from both each other and the old themes). In a lampshaded (in the Viral Marketing) instance, before fan complaints, the English dub was going to use the word "psychic" instead of "esper".
Unintentionally Sympathetic: The Computer Club President reaches Sheldon J Plankton-levels of this. While it was wrong of them to cheat in their challenge of the SOS Brigade, it was to get back a computer Haruhi stole from them using cruel blackmail.
Mikuru. She gets uprooted from her friends, family and timeline, is thrown into a culture alien to her without any of the technology she's used to in the future, where she is constantly manipulated, kept out of the loop and emotionally abused by none other than her future self. Add to this the fact that before being sent back in time, she underwent mental conditioning preventing her from ever revealing anything details of her old life to any of her new friends, no matter how much she might want to. And all of this abuse came from the people she's supposed to be saving. As of the end of the 11th book, there is hope for Mikuru now, as Kyon secretly hopes to find a way to safely alter time so that Mikuru doesn't grow up to be like her manipulative future self.
Also Yuki Nagato, and to a lesser extent, Itsuki Koizumi in The Disappearance Of Haruhi Suzumiya. Hell, everywhere after Yuki's Hostile Show Takeover and during the "Endless Eight" arc.
Jerkass Woobie: Before the start of the series Haruhi painfully realises that her experiences are mundane and not anything special (which is what she desires the most in her life), and in her quest to make her life special, goes on the hunt for aliens, time travellers and ES Pers after some inspiration from Kyon. This leads to her general bluntness, and her obsession with cosplaying Mikuru. And all the exciting things she's hoped for ARE in her life, but she's Locked Out of the Loop!
Woolseyism: The quote at the top of the main page more literally translated would have Haruhi asking for people from space, people from the future, people with special powers, and people from other worlds (although "alien" and "esper" are fairly standard translations of their respective Japanese terms).