goon I've watched quite a lot in recent years, but it's a hard question to answer because there are so many genres, just like in other mediums.
Fullmetal Alchemist: Brotherhood is kind of a safe choice to get into it (and I don't mean that in a negative way, it's still one of the best I've seen). Vinland Saga would probably also be a good starting point, although there are only two seasons currently so it's not finished.
Personally I can enjoy just watching how insanely good some of the animation is, so then Demon Slayer would be my first choice. However, the story isn't anything special and one of the side characters is very annoying.
From comedies, Kaguya-Sama is probably my favorite.
Made in Abyss is very good, but some things there are so disturbing that it's not something I'd lightly recommend to people. So I don't.
But you can't go wrong with Attack on Titan, really. It also has the benefit that you know you'll get the full story without the show being cancelled.
Cyberpunk: Edgerunners is probably the latest one to break through to the "mainstream" of non-anime watchers due to being of Netflix and because viewers could choose between English and Japanese right from the get go. Although not an anime, Arcane, also on Netflix, is a fantastic animated show.
I haven't watched much older stuff.
Edit: These are all shows. For movies, the Ghibli ones that BW mentioned are a safe place to start. Or, a personal favorite, Perfect Blue.
