What's the greatest (non-mecha) sci-fi anime?

Sorry about the late reply, for some reason I didn't see this until I was notified of a different response to a completely different comment just hours ago. I tried to get a variety on here of some shows that really hit the spot for me -- they might not all do it for you and I'd wager you've already seen a fair amount of them, but hopefully there's something fresh here that you'll enjoy! If you've got any to add, please let me know as I'm always looking for more to add to my watchlist.

Note: This is PART 1 of my response. Since it's too long for one comment, I'll reply to my own comment here with PART 2.

1. Sci-Fi:

• Parasyte: The Maxim (2014) - Another series that uses a Sci-Fi storyline to explore philosophical themes and concepts. While not always as eloquent at exploring its ideas as something like Psycho Pass, it still objectively examines what it means to be human, if a species’ prime directive can be viewed as “bad” or just part of nature, as well as surrounding considerations that I won’t spoil here. All in all, it’s a fun ride with interesting viewpoints and is worth checking out. Bonus points: it only has one Ecchi moment that, while out of place in the series, at least happens and is out of the way in the first five minutes of the series.
• Cyberpunk: Edgerunners (2022) - Set in the world of Cyberpunk 2077, this officially serves as a prequel to the game. Don’t worry though — you don’t need to have played the game or even need to be familiar with it. It stands on its own and isn’t afraid to show the consequences of living in such a gritty world. It hit me hard; I loved it, I cried, and the marketing tie-in completely worked as I became one of many to buy the game after watching this (which, luckily was patched up to a point of working just fine by then). The entire series flies by in a short 10 episodes so it’s a rollercoaster ride that fits into lots of different schedules, even if you’ve got a busy one!
• Cowboy Bepop (1998) - Let’s be real, you’ve probably seen this already so not much needs to be said. It’s one of the best future noir, space western, genre-expanding shows out there and is one of the few animes that I recommend to people that don’t like anime. I’ll usually watch both sub and dub without preference, but this is one of those shows where the dub really works best for me (and most of our introductions to voice actor Steve Blum). If somehow you haven’t seen it already, check it out now!
• Trigun (1998) - The other space western from 1998, Trigun holds up still. It’s not as accessible as Cowboy Bebop, but it’s still one of the best in my book. The alt. universe reboot, Stampede, is fun so far but has a long way to go before touching on the scale of the original.

2. Inspiring:

• Mob Psycho 100 (2016) - Easily in my top ten completed anime series of all time. Created by ONE (creator of One-Punch Man), this is one of those shows that makes me want to be a better person. It follows its character with genuine heart and only gets better as it goes on. Also, Season 2 has the best fight choreography for someone with teleportation powers that I’ve ever seen. BONES went all out with the animation for Seasons 2 and 3.
• Assassination Classroom (2015) - This is actually what got me back into anime after years of not watching any. I saw it on Hulu, thought it looked interesting and ended up loving it. A powerful, tentacled being will destroy the world in a year, but gives humanity a chance to save itself by becoming a homeroom teacher and challenging his students to find a way to kill him before the year is up. The storytelling impressed me on multiple levels, but most of all because there are no loose ends when it’s all done. Every question is answered, every students’ mysteries revealed, all paced in a way that makes it that much sweeter by the end. There were times where I’d have a question in the back of my head and get the answer 20 episodes later. It always gets to it. That coupled with a satisfying ending put anime back on my radar after a long break.

3. Psychological:

• Paranoia Agent (2004) - From Satoshi Kon, the “David Lynch of anime” behind movies like Paprika and Perfect Blue. Overworked and stressed out people keep getting attacked by a criminal dubbed “Lil Slugger” by the news. The catch? Lil Slugger doesn’t actually exist and was made up by the first victim. As more people claim to have been attacked, more stories and fear spread about the non-existent delinquent. Are the victims making this up for sympathy or are they manifesting his existence when they need it most? The ending is of course weird and might not do it for you (I'm still deciding how I feel about it), but the show in all is a unique experience and the only time Satoshi made a TV series before he passed.
• FLCL (Fooly Cooly) (2000) - A very short, very odd show when I first saw it. It has since been brought back for four more seasons that I have not seen, which may affect the vague and psychological elements of the original season, but for anyone looking for something out of the ordinary and for anyone that ever wanted a Rickenbacker bass guitar, this is worth taking a look at.

4. Action Horror:

• Castlevania (2017) - Yes it’s a US studio so maybe it isn’t actually anime, but semantics aside it’s a refreshingly fantastic video game adaptation. It starts out by actually making the audience very empathetic to Dracula, which makes his brutal mission of vengeance one that maybe we can’t condone but we can certainly understand. The first season is pure horror. The second season slowly blends in impressive action sequences until it’s a full-out action horror thrill fest until the series end.
• Chainsaw Man (2022) - This one isn’t for everyone. If you can put yourself in the shoes of the protagonist, whether through understanding his newly found access to being able to have a life of his own, or at least remember your hormones in high school, then his goals and motivations will add to the story. Otherwise, his motivations might just feel silly and juvenile (despite the fact that, in a way, juvenile is how it’s supposed to feel). Fantastic bloody action from MAPPA, though quite different from the look of Jujustsu Kaisen. However, similar to JJK, this one gives you two doofuses and one serious guy working as a team to fight the supernatural in style.

5. Action:

• JuJutsu Kaisen (2020) - There’s a lot to love about this one, but more than anything it’s one of the most impressive efforts from MAPPA, with beautiful animation that will hype you up. Similar to Chainsaw Man, you get two doofuses and one serious guy working as a team to fight the supernatural in style.
• Samurai Champloo (2004) - The creator of Cowboy Bebop trades in future noir and jazz for a period piece set to hip hop. Tons of fun, absolutely dripping with style and one of the most re-watchable series in existence. If an episode of it is playing, I’ll watch it.
• My Hero Academia (2016) - Often described as “Otaku X-Men,” this show really knows how to put you on the edge of your seat. It’s not perfect and sometimes might be a little too ideological for its own good, but I absolutely love it despite its flaws. Sure it’s another anime that’s slow to start, but the last few episodes of the first season ramp things up into a thrill-ride that had me running around the room and somehow keeps pushing that even further for the next two seasons. It’s superhero stuff but it’s very clever at how it goes about it. I’ve rewatched this so many times; the satisfaction of feeling so enthralled every time makes it one of my favorites. BONES doesn’t always deliver on the animation quality they start out with after Season 3, but it still works just fine. The soundtrack is on my workout playlist because it makes me want to Go Beyond, Plus Ultra!
• One-Punch Man (2015) - Created by ONE. While I consider Mob Psycho 100 to be ONE’s heartfelt masterpiece, One-Punch Man goes a different direction: a satire of superheroes and any anime protagonist that wanted to train to be “the strongest ever.” If satire is a kind of comedy you enjoy, this is a good time. There’s definitely a reason this became one of the most popular properties.