Alright, I am guessing I am probably older than the average person that might be posting here, so, for me, when I hear “older anime” I think back to shows/movies pre-2000. Limiting myself to that criteria, here are some that come to mind (in chronological order):

• Grave of the Fireflies (1988) - If you have never seen this movie, then you should. Just prepare yourself to be an emotional wreck for a good while afterward. My first introduction to this movie was in 2001. Back then, on September 11, the school was gathered into the main auditorium after the planes struck the towers. For some reason, some teacher thought it was a good idea to show a movie to the students to keep them entertained. I never found out which teacher chose it, but somebody decided Grave of the Fireflies was the movie of choice for the moment. Yeah… It has made for an interesting anecdote at parties ever since.
• My Neighbor Totoro (1988) - This probably remains the easiest entry point into anime for non-anime watchers that exists. There are many that argue other Ghibli movies might be better in one respect or another, but I think this one is special due to how approachable it is for just about any potential viewer regardless of age/gender/previous anime exposure.
• Yu Yu Hakusho (1995) - In my opinion, this series took a lot of the shonen conventions established by its predecessors like Dragonball (1986), and refined them. I am not about to claim it is the best shonen, but it established a lot of the best practices so to speak for what makes a good shonen and its influence can still be seen in shows today.
• Cowboy Bebop (1998) - This one is a classic by just about any definition. It is still talked about regularly in forums like this one. If that isn’t still relevant, then I don’t know what is.

Having pushed Earth to the brink of environmental disaster and overpopulation, the central government segregates the populace. The wealthy and well-connected get to remain as they are, but billions of everyday working folks get forced into artificial, self-contained living spaces over the course of several decades. Some of those spaces remain relatively comfortable. Many are densely populated, and some of the most isolated don’t even get natural sunlight. None of them have any say in how they are governed. This breeds unrest.

In the most remote communities, there is a growing push towards being self-governed. In tandem, the idea that their half-century plus of environmental isolation is pushing a new evolutionary path for humans starts taking hold. The champion of this ideal is a charismatic politician, who uses the notion of a higher-evolved humanity as justification for independence. Amid tensions with the corrupt, complacent central government, the politician dies suddenly. Both movements are then co-opted by populist fascists, whose leading family has effectively complete control of the local military. This leads to the deadliest, most brutal war humanity has ever seen.

This is the setup for Mobile Suit Gundam (1979), and yeah, I’d say that’s still pretty relevant.

Planetes.

I just realized Fullmetal Alchemist is over 20 years old, fuck I’m old ;_;

Evangelion feels shockingly modern in its storytelling considering it’s almost 30 years old

Serial Experiments Lain. Came out before smartphones and yet predicted a lot of modern technology. It’s a fantastic look at how tech can shape our reality and mental health.

Samurai Champloo for the vibes

Revolutionary Girl Utena. I recently re-watched some of my favorite episodes again (for many times over the years) and can still discover new things that I wasn’t aware before. The anime just keeps giving everytime I watch it and refuses to get irrelevant ever.

“relevant” is very broad and subjective.

I think they all stay relevant. As a product, as art, as history, as entertainment.

Ghost in the Shell (1995)

Outlaw Star for a universe that contains balanced tech and magic.

Metropolis (2001 film) - directed by Rintaro, loosely based on Osamu Tezuka’s manga

• this another anime film that I’d recommend going in blind if you can

also for anyone who enjoyed it or wants to dive into the rabbit hole afterwards here’s a link for you! The Temporal Messages of Metropolis

I’m not really an anime person, but Grave of The Fireflies will probably always be in my top 5 movies list.

JinRoh

Tell me a modern anime that’s relevant. They’re all titties and formula. 5-6 people, one awkward, one bold, one nerd, one tomboy, one stalwart, and a boy who’s confused.

So boring.