Anime

Grave of the fireflies

Can’t go wrong with just about any Studio Ghibli film.

Psycho Pass season 1 only

Honestly, everything that isn't a (battle) shounen should be great. The most important thing is to firmly establish that anime is a "medium" and not a "genre". And since almost every outsider thinks every anime is a battle shounen, it's important to correct that misconception early on.

AnoHana would be my recommendation. It's short for a series, it doesn't take any Japanese cultural knowledge to enjoy it, and the themes are universal regardless of personal background, age or gender.

Frankly speaking I expected a lot of Boku no Pico recommendations. Where are they?

My non weeb friends liked Frieren, Cyberpunk Edge Runners, and Deathnote. I'd also recommend Serial Experiments Lain if you want something that forces you to think about it to understand it.

I liked Kimi Ni Todoke (apparently translates as from me to you) and think everyone should watch or read it.

I find that SpyXFamily and the Ghibli movies are what most people best relate to though, so if it's a question of getting someone hooked start with *Spirited Away, Kiki's Delivery Service or Howl's Moving Castle. *

I'd recommend things based on stuff they like to read/watch in other media, so I don't have a single must-watch.

That said my initial picks would be Fullmetal Alchemist: Brotherhood, Spy x Family, Kimetsu no Yaiba, Nichijou. Perhaps Log Horizon? EDIT: Uzumaki for people who are into suspense/horror.

I wouldn't recommend it as a first anime to most, but I introduced a friend to anime with Spice & Wolf

Odd Taxi

I like to be sadistic and recommend getting into Gundam

oh man. you know someone said deathnote and you know. Imma go with that.

Throw them into the deep end: Golden Boy.

haruhi, hyouka, angel beats, puella magi madoka magica, frieren

your name along with other shinkai makoto films are also great

i guess some of these are too weeb-ish tho, lol

Maybe the show that you could make the most references to while watching other anime? So JoJo’s.

"Vash the Stampede".

Gurren Lagann

One Piece or no balls

Full Metal Alchemist: Brotherhood. I think if someone wants an easy introduction to a large chunk of what anime is like, FMA:B delivers while standing alone as a very solid piece of media regardless of medium.

For me, it's gotta be none other than Cowboy Bebop!

• It's a fantastic sci-fi series that's gritty and realistic without taking itself too seriously.
• The world-building is top notch, the cast of characters are extremely likeable, and the dialogue is memorable.
• It's truly got something for everyone--kung fu, gunplay, ship battles, western, noir, comedic moments, drama, supernatural elements, immaculate vibes, etc.
• One of the best soundtracks of any show ever, famous for "jazz" but actually mixing a wide variety of genres and styles.
• Some of the best cel animation and painted backgrounds from the legendary studio Sunrise, with tasteful uses of early CG.
• Only 26 half-hour episodes, plus one optional film and one optional bonus episode.
• Mixes stand-alone episodes with a extremely satisfying longer story arc that will certainly leave you feeling something.
• Good performances in both the native Japanese, as well as the stellar English dub that was ahead of its time.

Cowboy Bebop seems to be the anime that transcends the genre more than almost anything else, and appeals to people even if they don't typically gel with more tropey anime. I really think that Bebop is a triumph of the medium and one of the best television shows period, so I really can't recommend it enough to everyone!