I’d classify a must watch as something everyone should see, not just fans of the genre.
The only must watch shows are FMA Brotherhood and Cowboy Bebop. As for movies, I’d really only list Ghibli films like Howl’s Moving Castle and Spirited Away.
I agree with both @Unboxious@ani.social and @falidorn@lemmy.world regarding the definition of a must-watch anime. There's nothing that can please everyone, and yet there are some things everyone should have at least heard of. Hearing of something may be a low bar, but it is the precursor to attempt watching it.
To put it another way, this question is asking for the greatest (read: most popular) of all time for anime.
It's hard to call something a "must watch" because different people like different genres. If we define "must watch" as something every fan of the genre should watch, my list would be Redline, Gurren Lagann, LOOK BACK, Kaguya-sama: Love is War, and Skip and Loafer.
Oh man, I'll give plenty of recommendations, where to start?
I think the best things to come out in the last year are Dungeon Meshi and DanDaDan. Both are at a level of quality and originality that I'd feel comfortable recommending them to anyone who likes anime. Neither are finished, but both come from animation studios with a very high pedigree who I trust to continue doing great work.
I'll also always recommend GOATs like Fullmetal Alchemist: Brotherhood, Death Note, Cowboy Bebop, and Evangelion* pretty freely. Evangelion comes with the asterisk because I warn everyone how heavy it is, but I'd still push anime fans to go through it once because of how great it is.
Lastly, there's a few I will recommend with many caveats. Stuff like JoJos Bizarre Adventure, One Piece, Panty + Stocking, Gurren Lagan, are all really, really great interesting and unique anime. They also have a lotta gooner bait in them. Sometimes it's because the show is trying to to satirize gooner bait, sometimes it's because the author is both a gooner and a talented mangaka, but I will give heavy warning beforehand and will usually only recommend these shows to people who watch a lotta anime.
I am gonna throw something random out there that I am watching rn since I don’t see it mentioned- Galaxy Express 999. It is episodic but has an over arching plot and the stories are really well written.
Mine would be anything directed by Yamada Naoko, this includes:
Silent Voice
Liz and the Blue Bird
Tamako Love Story
Kimi no Iro (if you live in USA, it'll be in theater on 25th Jan)
K-On
Heike Monogatari
Modern Love Tokyo episode 7 (Modern Love Tokyo is an anthology of love story by various directors, most is a live action drama except episode 7, so you can jump straight to episode 7)
Hibike Euphonium (Yamada was the series director for 1st & 2nd season, but give the 3rd a watch as well, it's cinematography best to none for me last year)
Hibike! Euphonium was directed by Ishihara Tatsuya, who has also done a bunch of other must-watch anime.
Kanon 2006, Clannad, Haruhi Suzumiya, Nichijou, Dragon Maid S, and of course Hibike! Euphonium.