I thought about highlighting three specific anime.
Cowboy Bebop
Its episodic nature did make me turn off on it the first few times. Finally a few years ago I kept watching and finished it. Everything in an episode is carefully planned out. The music and the show are linked together. Then there is the hollow feeling when the bounty hunting stop. That's the moment you realise that all those adventures made you part of the experience.
If you would just focus on the main plot then it wouldn't get that much impact. It's about bounty hunters getting caught in strange shit. Some of it ties directly back to the characters, other episodes are just funky shit like mushroom hunting.
26 episodes and a movie makes Cowboy Bebop easy to recommend. It also looks fantastic on blu ray.
Legend of the Galactic Heroes
Just saying it's unique is not enough. The adaption of a series of novels spanned 110 OVA episodes. Multiple animation studios went through this series. People would have to mail order these episodes just to watch it.
The scale and ambition of this project is huge. A giant space epos that details a cast of about 50 people. All of them have their history, character motivations and especially character growth. It's about the complexity of 100 Naoki Urasawa works tied together.
It has romance, drama, politics (still relevant!), space battles (with or without inertia), history, world building and tons of other stuff that make LOGH a very intriguing watch from start to finish. You see multiple sides of war from different viewpoints. You'll care about the Empire and the Republic. Don't get too attached to your characters though, they die faster than in a regular GoT season.
Of course it has its flaws when dealing with an one dimensional religious villain, but that's easy to forgive for its time imho. I would even give this one a 11/10. Stuff like this doesn't get made again.
The new series can't measure up to this in a million years. LOGH is a treasure from its time for those that are crazy enough to follow up on it.
Lupin III: Castle of Cagliostro
The Lupin III franchise is just plain fun. Gentleman thief Lupin III is the grandson of the famous Arsene Lupin. He pulls of all kinds of crazy heists together with his partner Daisuke Jigen, a gunsman with pinpoint accuracy. Occasionally joined by swordsman Goemon Ishikawa and the mysterious Fujiko Mine.
Of course every force has to be brought to balance. The police detective that tries to capture Lupin is Koichi Zenigata. Sometimes he succeeds, but most of the time he fails. Lupin III can be thought of as a Japanese version of James Bond when you introduce a Tom & Jerry like dynamic.
Lupin like his predecessors announces the crime before it happens. To give the other party the idea that no matter what they do, you can't stop the theft from happening.
Not only does Lupin get in trouble with the cops, several crime syndicates are also after Lupin and his gang.
Now Castle of Cagliostro is a film that encompasses everything I like about Lupin III and it looks like fun. This was directed by Hayao Miyazaki and I think it's one of his best movies ever made.
Maybe I'll make another post with some of my other favorites, as this post is getting a bit long already.