It's been a while since I've watched Haruhi, but I believe the name itself carries a lot. The Melancholy of Haruhi Suzumiya is a classic, and is worthy of a spot on this list.
Let's begin with the premise. Haruhi (as I will refer to the show from here on) follows Kyon, who somehow finds himself tangled up with Haruhi Suzumiya, a whackjob who's wants to hang out with aliens, time travelers, and espers, who she actually believe exist. However, it turns out that aliens, time travelers, and espers do exist, and all of them are interested in Haruhi, since apparently she's God, or a God of some sort. Long story short, Kyon becomes God's wrangler, and the show follows his attempts to keep Haruhi satisfied through various schemes and plans she comes up with.
There's a lot to be said about Haruhi. The characters are as iconic as the show itself. Kyon's neutral personality balances out Haruhi's eccentricities well, and the supporting cast of Mikuru, Yuki, and Itsuki each highlight the surreality of Kyon's situation. Mikuru is a sweet time traveler who can't tell him anything, Yuki is an alien robot who knows everything (and is typically the one who gets stuff done), and Itsuki is a shady-ass esper who you can't ever get a read on. The dynamic of the group, however, falters at time given how Haruhi is literally God, and everyone has to appease her or the universe might literally end, and I think the show suffers because of that. Haruhi is, at times, absolutely insufferable, and made the show difficult to watch at times. I personally like the theory that Kyon is an unreliable narrator, which would explain why Haruhi is insufferable (since it's all from Kyon's POV), but, regardless, Haruhi is insufferable and the show is difficult to watch at times because of it (hence why it's so low, I'll get to the second reason shortly).
I am including the movie The Disappearance of Haruhi Suzumiya in my rating as well, since that's an actual arc in the source material. The movie provides much desired characterization for Kyon and really does make me believe he's an unreliable narrator, as his desperation to find Haruhi and continue his life with her is completely out of character with how he acts in the series. It does go to show how much he enjoys his crazy life despite acting the stoic. If there's one thing to admire about Haruhi it's that the characters feel human.
Haruhi is arguably
THE anime that takes place in a High School, so while the trope is cliche at this point, Haruhi kinda defined the trope, so no points off. They also use the setting well, and it results in God Knows,
arguably one of the best and most iconic songs in all of anime, so points gained.
I have to give special mention to the Endless Eight arc, which is just...
why did they decide to do what they did with that (I'm not spoiling anything about it)? Just, watch out for the Endless Eight.
You've been warned. Lots of points are lost for Endless Eight tbh. I got like 5 episodes in when I realized you only need to watch the first and last. There's a reason I had to look for that answer.
Besides losing points for the occasionally insufferable Haruhi and the Endless Eight, the reason it's so low is because, to put it simply, for one reason or another I like the other anime on this list more.
Also, this isn't related, but I'm gonna trash on the spin-off about regular Yuki. It's garbage, and any universe where Yuki Nagato can't shred on a guitar is a bad one.