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My favorite is Hunter x Hunter. I love the explanation of their powers and growth. The way things are thought through and broken down is so cool. The plot is full of intrigue and surprises. And it's a really fun world to get lost in.

Sailor Moon and Ronin Warriors! The former sparked my love of short-haired pixie cuts on women (Sailor Mercury, I think) and the latter sparked my love of redemption arch in storytelling!

(In know these are not the type of anime referenced in the question, but these were my first experiences with anime and stick with me like my first lay.

My absolute favourite is definitely The Ancient Magus' Bride but close second and third would be Spirited Away and Princess Mononoke.

Patlabor movies 1&2: extremely realistic mecha and pretty deep story, though they are really slow and don't have the explosive pace most action animes bring. I love them still. There's also a very good abridged version of Patlabor 1 on YouTube, it's hard to remember the actual movie after watching it.

Ghost in the Shell movie, GITS Stand Alone Complex and Second Gig are also extremely good. In a way they are one of the definite sources of modern cyberpunk - though hardly the first, the inspiration they brought can be only compared to Star Trek imo. There have been GitS stuff since, but they never managed to recapture the same heights.

And if you like more modern stuff, 86 is one of my favorite shows of late. The base story isn't bad - it clearly has a lot of thought put into it, but it feels somewhat bland in parts - but the way they brought it to anime was just sheff's kiss. It's ridiculously well directed. That said, you need to have a certain appreciation to bleaknees and some (melo)drama to really enjoy it.

No game no life

A lot of decent ones have been mentioned so I'll add a few I didn't see:

• Keep your hands off Eizouken: I can't express my love for this one enough; it's beautiful, touching, funny, and just one of the most lovely things I've ever seen.
• Bocchi the Rock: very funny, and extremely uncomfortable for introverts but in a good way
• Delicious in Dungeon: extraordinarily good adaptation of the manga; this one isn't done yet so who knows but it's wonderful so far, and Studio Trigger's animation won't disappoint
• BNA: another Studio Trigger, lovely animation. I love how this one almost makes a point several times and then just glances off of it; it's a bizarre one

Star Blazers:

https://youtu.be/rz263xIQmvo

Maybe Battle of the Planets:

https://youtu.be/acOnskcyrtA

There is no such thing as "the best anime", all you will hear are peoples personal biased opinions. With that being said, ill give you multiple options for different genres, cause ya know, the above.

Animation: that one goes to akira for me, quite breathtaking gorgeous visual, form the backgrounds to the silky smooth characters, special shoutout to the dude who had to draw tetsuos mutated nutsack.

Fun factor: Ben-to, from the makers of tje jojo animes, smooth action, impactful sound effects and just straight fun seeing people beat the shit out of each other for price reduced food

Action: Claymore, that one might ruffle some feathers, but love it or hate it, the fights are high octane, brutal and had me at the edge of my seat despite knowing the manga (especially teresa vs the other 4)

Mystery: Gosick, basically little female sherlock homes, the cases she solves are an intriguing watch if you like that sort of setting

Feeling like a child again: Little witch academia, have you ever had the feeling when you watch something it made you feel young again? be it for the setting, the feeling or just straight of nostalgia? for me LWA gave me a glint of a childlike wonder i havent felt in many years

cute girls doing cute thing: None can come even close to Girls und Panzer, adorable character design, next to zero fan service, accurate panzer action (for the most part) and the battles are just generally SUPER good

and lastly: Bawling your eyes out: Ano Hi Mita (the flower we saw that day), an estranged group of friends lost oen of their people, years later they find common ground again by trying to fullfill their lost friends last wish, i still bawl like a little baby girl who just saw spongebob dry out on the fishermans table at the ending

for anyone who finds something new to watch with this, my job here is done

Any of Satoshi Kon's works (Paranoia Agent, Perfect Blue, Millennium Actress, etc). IMO, he's one of the few animation directors who really takes advantage of everything animation has to offer.

Edge runners, erased, code geass, death note, monster, Boku no hero academia, one piece, azumanga daioh, banana fish, re:zero, steins:gate, Hunter x Hunter, mob psycho

This list will keep you at the edge of your seat for a year

Beastars is the only anime I’ve ever rewatched. It’s just great.

Either Naruto or Death Note. I'm just a sucker for animes with characters trying to outsmart eachother.