The first entry on this list brings us a combination of space travel and westerns. The series follows a group of bounty hunters, Spike Spiegel, Faye Valentine, Jet Black and Edward, who hunt criminals across space. The Cowboy Beebop anime brings a great self-contained story in each episode while hinting at a larger story. The series came out in 1998, so it looks a little dated compared to modern standards, but the story holds up as a cool space story.
Dr Stone is a great series exploring what life would be like from 0. In the world of Dr Stone, our protagonist Senku and the rest of humanity have been petrified for 3,700 years. With modern innovations lost to time, Senku and his friends must start building science back up. The series is genuinely interesting and brings us a great primal world with mysteries surrounding petrification.
Parasyte: The Maxim
Parasyte is a series set in the modern world, where a new species of creatures takes over the bodies of its victims. Parasyte is a great series if you love body horror; the designs of the creatures evoke scenes from The Thing; this is mixed with the struggle the protagonist Shinichi goes through with an alien parasite infecting his hand as a literal interpretation of alien hand syndrome. Parasyte: The Maxim is a great alien invasion story, told from the perspective of a single character and is perfect if you are in the mood for some extra-terrestrial violence.
Code Geass: Lelouch of the Rebellion
The next entry on this list brings us a story set in the not-so-distant future, where giant mechs are commonplace. The series follows Lelouch vi Brittania as he mounts a rebellion with a resistance movement. Code Geass brings a supernatural flair to the genre by giving the protagonist Lelouch, the ability to give a single command to anyone he sees. Code Geass is an amazing story told from the perspective of a deviously intelligent protagonist as they take on the corrupt government of Britannia.
Psycho-Pass is set in a dystopian future where your mental health decides everything in your life, from your career to your societal position. The series follows a squad of police officers as they use futuristic weapons called Dominators to take out dangerous criminals. It's an interesting series exploring mental health, morality and the idea of the greater good.
A mad scientist, time travel and alternate timelines all amount to a fantastically mind-bending story with a wonderfully complex story. The story follows Rintaru Okabe and his reluctant team of friends as he invents a device that lets him send text messages back in time. Steins; Gate brings us a great story with a complicated cast of characters that will leave you wanting more, which is good because Steins; Gate is followed up with a film and a sequel series following one of the alternate timelines explored in the anime.
The Promised Neverland
The Promised Neverland displays the loss of innocence, unlike any series I've seen. We follow the cast of children, barely 11 years old, as their world collapses around them. We see the characters fall apart and see the people they thought they could trust betray them. The sci-fi in The Promised Neverland is more subtle than the other entries on this list, but we can see it when we make our way through the story.
Legend of Galactic Heroes
The last entry on this list is perhaps the oldest, with its release in 1988. The series was adapted from a series of ten novels. Suppose you are looking for an interstellar war between a galactic empire and an alliance of free planets. The story is an idealistic struggle between strategic masterminds who clash in this interstellar conflict.