I see nobody mentioned any good animes yet, so I'll start: Death Note, Code Geass, Puella Magi Madoka Magica, Columbo, JoJo's Bizarre Adventure (both the older OVAs and the newer full series).

Tsee………

Why does anime look "like that?"

• Astro Boy
• Kimba the White Lion
• Sazae-san
• World Masterpiece Theater
• Lupin III

Should at least be a start. Those first two are works of Osamu Tezuka, the "godfather of manga", so they were especially influential in creating the standard practices and visual language of anime and manga.

You can also check out Aggretsuko and Kemono Friends as two anime that buck the typical "anime style" in one way or another, and also Panty & Stocking with Garterbelt, which will come up again later.

Why are there so many cute girls?

To trace the historical development of moé and "waifu" culture, these works in order:

• Urusei Yatsura
• Gunbuster
• Project A-Ko
• Nadia: The Secret of Blue Water
• Neon Genesis Evangelion
• Azumanga Daioh
• The Melancholy of Haruhi Suzumiya
• Lucky Star
• K-On!

While you're already watching so many shows by Kyoto Animation, you might as well throw in Nichijou and Clannad, too.

You can also take a swing after Evangelion to watch

• Tengen Toppa Gurren Lagann
• Panty & Stocking with Garterbelt
• Kill la Kill
• Little Witch Academia

I just wanna know the memes!

• Jojo's Bizarre Adventure
• Kaguya-sama: Love is War
• SPY x FAMILY
• Toradora
• Steins;Gate

These are anime that are either extremely popular today or were extremely popular in the 2000s or 2010s, and spawned a lot of enduring Internet memes.

Edit: Ghost Stories is known for its dub, but like… Honestly, it's probably better subbed. The hashtag edgy jokes in the dub can be funny as clips but it's kinda tedious to watch as a show IMO.

Tell me about some auteurs or great directors!

You've already seen or been recommended other works of Satoshi Kon (Paprika, Perfect Blue, Tokyo Godfathers etc) and Shin'ichiro Watanabe (Cowboy Bebop), so to add to them I will mention Paranoia Agent and Samurai Champloo. The latter is also notable for being a major inspiration on The Boondocks.

Your Name is the first of Makoto Shinkai's "disaster trilogy".

Akiyuki Shinbo is a famous anime director known for frequent use of techniques like collage. Some of his most famous works include Bakemonogatari, Puella Magi Madoka Magica, and Hidamari Sketch.

Other works of Isao Takahata and Hayao Miyazaki have already come up elsewhere in this thread, so I will mention

• Lupin III: The Castle of Cagliostro
• Nausicaä of the Valley of the Wind
• Spirited Away
• Howl's Moving Castle
• My Neighbor Totoro
• Grave of the Fireflies

There's also these works of Mamoru Oshii:

• Angel's Egg
• Patlabor
• Ghost in the Shell
• Urusei Yatsura

If you're already watching Urusei Yatsura, and have already seen Ranma ½, you might as well add Maison Ikkoku and InuYasha to your list as other adaptations of Rumiko Takahashi, one of the most successful women manga artists of all time.

Introduce me to some genres!

For magical girls (mahô shôjo):

• Cardcaptor Sakura
• Ojamajo Doremi
• Precure
• Tokyo Mew Mew

For anime aimed at girls where the girls aren't magical: Kodocha has my personal recommendation, Fruits Basket is extremely popular.

For idol anime, there's Idolmaster and Love Live.

For iyashikei, there's Yuru Camp, Yokohama Kaidashi Kikou, and ARIA.

For yuri, Kase-san and Morning Glories and Bloom Into You.

Anything else?

Stop!! Hibari-kun! is notable for having a pretty well-written transfem protagonist for an 80s anime.

Summer Wars is a movie I never cared for, but a lot of other people like it.

And also, everything everybody else has mentioned in this thread.

Edit: Added and moved around a few titles; I wrote this in a bit of a hurry.

Other comrades already gave a lot of great answers so I just want to give my thumbs up for these in special:

• Trigun is pretty cool, I have yet to watch the movie but I heard it was good and the new anime Trigun Stampede is genuinely great too, I have to watch the second season that aired not long ago.
• Evangelion is a must. If you haven't watched it yet, I recommend you look up the order to watch the anime finale because you have to watch a movie to properly finish the anime, then I recommend you watch the Rebuild movies which in my opinion are even better than the anime. Obligatory Communist Eva edit someone posted sometime ago.
• Revolutionary Girl Utena is regarded as an absolute gem of a classic for a reason, I would know my online nickname is the opening song of the show lol, also obligatory AMV. Watch the anime then watch the movie. This series is kind of known as the older sister of Evangelion and both authors are pretty good friends.
• Cowboy Bebop deserves to be watched, it's simply incredible, including the movie.

For newer stuff:

• Gurren Lagann is absolute peak, I recommend you watch the anime first then watch the two movies which in my opinion just elevates it even more. Anything by Studio Trigger tend to be pretty good in general.
• The movie Redline is bonkers and absolutely incredible.
• Also the movie Perfect Blue, just trust me on this one, it's amazing, pretty dark, but amazing.

Ghost In The Shell is a classic for a reason.

Slayers is genuinely funny.

Kino's Journey (2003) is the story of an enby and their talking motorcycle visiting a series of philosophy/science fiction thought experiments, seeing how fucked up those are, and seeing the beauty in that.

Rose of Versailles is an early and shockingly influential anime about the french revolution that Sailor Moon and Revolutionary Girl Utena shamelessly steal from. the 2000s anime L'Chevalier d'Eon is a homage/prequel to it in many ways.

Oh yeah, Revolutionary Girl Utena is essential watching. Also Code Geass

Some older stuff that I didn't see mentioned (and bulletpoints since everyone's being so neat):

Metal Skin Panic MADOX-01

• A comedy about a schmuck trying to visit his girlfriend who accidentally gets stuck inside a suit of power armour. The suit design was blatantly ripped off by the rpg game RIFTS (among others).

Cyber City Oedo 808

• Three short cyberpunk films about some badass prisoners too goddamn cool to stay in space prison, given bomb collars, and suicide missions. Great intro theme. Perfect Shadowun inspiration.

The Big O

• Batman with a Giant Robot, basically, but gets rather bizarre later. In a domed post-post-apocalyptic city where everyone lost their memories 40 years ago, Bruce Wayne works as a high-stakes negotiator and moonlights as the pilot of a giant robot to punch the unusually large number of rogue giant robots that keep getting dug up (and seems to single-handedly keep the construction industry afloat with the pretty realistically massive damage the fights do to the scenery).

Newer Stuff:

Land of the Lustrous

• I always recommend this. A post-post-post-post-apocalypse earth produces three successor races to humanity. One of those is a kind of animate gemstone coral, immortal, androgynous, photosynthetic, and hunted to make into jewellery by cruel things from the moon. One day the youngest, with a fragile body, decides that they want to change.

Have you seen Trigun?

i havent watched anime in a thousand years so i dont remember many, but have you seen these?

• azumanga daioh
• tengen toppa gurren lagann
• flcl
• cromartie high

• Akira is a must-watch for any cinephile, period. A lot of CGI techniques were invented during this film's production, causing it to go wildly overbudget. No Akira means no Jurassic Park or Toy Story.

• Anything by Satoshi Kon. People have already mentioned a some of his works in this thread, like Perfect Blue.

• Anything Studio Ghibli (also mentioned ITT).

Please note I'm heavily biased towards horror and watch a lot of it. So, the horror recommendations:

• Another (2012): A new student encounters a mysterious girl in his class who no one else will acknowledge exists.

• When They Cry (2006): A small country town is plagued by a horrible curse. Warning: extreme violence against children. On the third or fourth episode (I forget which), something very weird is going to happen and you'll be wondering if there was a mistake. Keep watching, it will make sense.

• School Live! (2015): A group of girls starts the Life Club at their school. Except something isn't right.

• Flowers of Evil (2019): One day middle school student Saeki impulsively steals his crush's gym uniform. But before he can correct his mistake and return it, he's blackmailed by his classmate, Nakamura. Nakamura is an absolute sociopath and she will traumatize anything and anyone around her. She will continue to escalate Saeki's situation more and more until his life spirals out of control. At what point, however, do you stop being a victim and start becoming an accomplice? Serious SA warning as this series is heavily themed around consent or the lack thereof. It also didn't get a second season to finish adapting the manga, where things continue to get worse before having its amazing ending.

• The Promised Neverland (2019): An orphanage isn't what it seems. Season 1 is one of the best animes of all time. Do not watch season 2. Season 1's ending is perfect.

• From a New World (2012): Students at a magical school discover a terrible secret hidden from the rest of their post-apocalyptic society.

• Shigurui Death Frenzy (2007): Two samurai, one blind and one missing an arm, confront each other in a duel to the death at a tournament hosted by a daimyō gone mad. The series focuses on how their rivalry started and how they got their physical injuries. It's an unapologetic look at the samurai and the caste system of Japan. Pretty much all of the warnings, however. It gets pretty graphic.

• Erased (2016): Satoru travels back in time to when he was 10 years old to solve the disappearance of his classmate and his mother's murder.

A few I haven't seen mentioned yet:

Memories - 3 short films from the creator of Akira

Now and then, Here and there - Extremely depressing isekai before isekai was a thing

Haibane Renmei - Atmospheric village life with some magic

If you liked Cowboy Bebop, then Samurai Champloo and Space Dandy are both must-watch.

Space Dandy, Project A-ko, Dirty Pair, Record of Lodoss War, Gurren Lagann, Macross, Fist of the North Star is proto Jojo.

As far as movies Perfect Blue if you don't watch anything else from this list, Night on the Galactic Railroad, Venus Wars, Wicked City and Vampire Hunter D has a few adaptations but they're all worth checking out.

If you like big mechs or gay women you owe it to yourself to watch the recent lesbian gundam anime, Gundam Witch from Mercury. It's a sort of modern staple.

I don't have many yuri recs (simply because a lot of the foundational works remain unadapted).I can suggest watching K-on, Sound Euphonium, and Bocchi if you like music or girls doing literally fucking nothing while making music.

It's not a staple like the slice of lifes I just mentioned but the recent yuri anime Kamiina Botan Blooms Like a Lily When Drunk is a big collage art project that really shows how different directors and animators storyboard and adapt the same source material. Each episode has a new director, so you get different uses of the same visual space. I think it's a good way to see what kinds of art direction are taken in modernity and potentially find new directors you might like. Also, it's gay as fuuuuck and about adult college students which instantly bumps it up a million points.

Haven't seen Wing, but I'd recommend the original 1979 Mobile Suit Gundam. It's sequels at the same-quels and prequel are all good at worst, amazing at their best.

Nichijou slaps

Project Ako, if you want a bit more obscure stuff Shadow Skill is cool too

There's a handful of movies you may not have seen. Paprika, Tokyo Godfathers (CW: Homophobia/transphobia, but also trans representation), Belladonna of Sadness (CW: Sexual Assault), Perfect Blue (CW: Sexual assault again). There's lots of other movies out there that are also very good, like the Ghibli stuff like Spirited Away and Princess Mononoke, the original Ghost in the Shell films.

For series, there's Serial Experiments Lain and as a bonus, clips from a public broadcast station in the US that showed it in the US for the first time, along with some other stuff.

All of Evangelion is good.

If you like Gundam, you could try Legend of the Galactic Heroes which is an extremely long (110~ eps) political space epic.

Monster is another really good one, but needs a whole host of content warnings depending on what episode you're on. It's not EVERY episode, but there are heavy themes of inflicting emotional and physical damage on children.

Revolutionary Girl Utena is another classic (CW: incest, emotional abuse, toxic relationships).

Some of these are older or newer than others and I'm more strongly invested in specific ones like Monster and Lain personally. Just more well known series I could think of off the top of my head.

The Berserk (1997 TV series) is one, plus the only good adaption of Berserk of all of them

People really like the 1999 Hunter x Hunter anime too

The original Bubblegum Crisis OVA is definitely worth watching. If you like it, also check out the American movie Streets of Fire which was heavy inspiration for BGC's style.

On to the suggestions!

Dirty Pair - Sci-fi action comedy. The adventures of two lady space cops as they get into sometimes-very-accidentally-destructive shenanigans throughout the galaxy. It's currently being aired on the hextube on saturday nights.

Ebichu Minds The House - A cheerful sentient talking hamster with zero impulse control or verbal filter does housekeeping chores for her unmarried world-weary office-lady owner. Ebichu is voiced by none other than Kotono Mitsuishi. She got the role because while doing recording sessions as Misato in Evangelion, she would cheer up the cast and crew by performing the Ebichu manga aloud.

Monster - Real-world social-commentary drama. This is a long series at 74 episodes, but I think it's worth watching. A kind and skilled Japanese neurosurgeon is a rising star at a West German hospital in the last years before Germany's unification. The doctor saves the life of a young boy who wasn't expected to survive a gunshot to the head, and then the doctor's life starts falling apart through no fault of his own. This is one I'd go in blind for. The story touches on matters of ethics, empathy, bigotry, justice, mercy, all kinds of very human stories. The title is purely metaphorical. The only monsters are humans.

Serial Experiments Lain - Sci-fi/technological social commentary. It's hard to categorize this one, it's one of a kind. This aged like a fine wine. Go in blind and keep reminding yourself that this series was planned out thirty years ago, when the idea of everyone having 24/7 access to the internet via pocket computers was pure fantasy.

Gunbuster - High school sports drama meets Top Gun meets The Forever War. Young adults are recruited into Earth's interstellar space navy to fight against ship-sized alien monsters trying to destroy humanity. The recruits gradually lose social connections with their family and friends back on Earth as time dilation effects pile up. There's a parallel/sequel series Diebuster made later, which has a very different animation style but I think is absolutely worth watching afterwards if you like Gunbuster.

Escaflowne - Magical-technological fantasy. Technically a high-school-girl isekai, but one of the best ones. There's a movie as well but it's one of those alternate-universe-retelling kind of things.

pre-Ghibli Miyzakai and Takahata stuff like Heidi, Anne Of Green Gables, Panda Go Panda, Future Boy Conan, Horus: Prince Of The Sun (really good), Taro The Dragon Boy (really good too), etc. etc. It's a good way to get into older anime that's also really good. That and Leiji Matsumoto stuff is usually a good entry point for '70s anime, like the Galaxy Express 999 movies (TV show is good too but it's long and repeats the same themes a lot).

Trigun, Initial D,

Hellsing, gothic vampire hunting in contemporary London. Alucard is one of those characters that’s constantly, as the kids put it these days, aura farming. They did a follow up series as well, only watched bits of it.

Maria-sama ga miteru is an historically significant work in the yuri genre. You could certainly still watch it today.

And not exactly what you're looking for but basically everything from Masaaki Yuasa is gold, The Night is Short Walk on Girl, Mind Game does interesting things with the medium, Inu-Oh is about a medieval Japan hair band and a cursed child.

golgo 13

A couple overlooked classics:

• Turn A Gundam
  • This is the best Gundam series, without question, but it's probably better after you've seen a couple other Gundams
• Macross Frontier
  • Essentially a more modern retelling of Macross (mecha + idol singers). It's great. The original Macross is the stupidest thing I've ever seen (laudatory), but MacrossF is just a great story.
• ReLIFE
  • The premise is horrifying. The implications are horrifying. The anime never even acknowledges that there could be anything wrong with it. Everything about the premise will turn you away.
  • Watch it anyway. It's probably the best romance anime ever made.

And some anti-classics:

• Maryuu Senki
  • The epitome of violent over-sexualized 80s OVA trash. It's horrible. I love it.
• Mad Bull 34
  • Police procedural comedy staring a murderous lecher. One of the most outrageous ever.
• Dominion Tank Police
  • Until this season's Ghost In The Shell adaptation by Science Saru, the only Shirow Masamune work to get a faithfully silly adaptation

Your list is pretty action focused. Not sure if that's your preference or just what aired for you. My recs would be

Ouran High School Host Club - A slice of life romcom.Transphobic language, but generally positive representation. It's an absurd comedy about rich students playing at being a Host club and the scholarship student they rope into their shenanigans.

Great Teacher Onizuka (G.T.O) - A moronic hooligan becomes the homeroom teacher to a group of twisted bully students and slowly wins them over. Be warned Onizuka is a creep especially in the first two episodes.