I'm surprised no one has mentioned frieren yet, it's probably the best anime of the last decade.
Gonna go for the 00's and older classics.
Record of lodoss war OVA (one of my personal favorites)
Tekkaman Blade
Shadow skill (movie is better but both show and movie are great)
Vampire Hunter D
Armitage III
Space Pirate Captain Harlock
Gundam X
Mobile Fighter Gundam Wing
Galaxy Express 999
Cowboy Bebop (obviously)
Robot Carnival (it's not so much a suggestion but a experience, it will show you how anime once was)
Tenchi Muyo! (was hesitant to post this, it's a good show but it's also more or less the founder of the harem genre)
The Vision of Escaflowne
Patlabor (movie, tv series, ova, patlabor is famous in japan for a reason)
Street Fighter II the animated movie
Venus Wars
3x3 Eyes
Ah! My Goddess (series, if you like romance)
I will also back up bubblegum crisis and cyber city oedo 808
For more modern anime:
Sousou no Frieren/frieren the slayer as i mentioned before.
Wotaku ni koi
Tsukimichi ~Moonlit Fantasy~
Ergo Proxy (if you like mind screw anime, this borders on 00's but putting it here as it was revolutionary at the time)
Zetsuen no Tempest (another psychological story, though not in the same way as ergo proxy)
One Punch Man (you've probably seen it)
Stein's Gate
Tensei Shitara Ken Deshta
The Unwanted, Undead Adventurer/Nozumanu Fushi no boukensha (like frieren it's hard fantasy and i love every second of it)
The Irregular at Magic High School (this one i'm kinda hesitant to suggest as while i like it, it's not for everyone, it's probably something someone who liked the more famous anime would like though).
Gonna go for the 00's and older classics.
Record of lodoss war OVA (one of my personal favorites)
Tekkaman Blade
Shadow skill (movie is better but both show and movie are great)
Vampire Hunter D
Armitage III
Space Pirate Captain Harlock
Gundam X
Mobile Fighter Gundam Wing
Galaxy Express 999
Cowboy Bebop (obviously)
Robot Carnival (it's not so much a suggestion but a experience, it will show you how anime once was)
Tenchi Muyo! (was hesitant to post this, it's a good show but it's also more or less the founder of the harem genre)
The Vision of Escaflowne
Patlabor (movie, tv series, ova, patlabor is famous in japan for a reason)
Street Fighter II the animated movie
Venus Wars
3x3 Eyes
Ah! My Goddess (series, if you like romance)
I will also back up bubblegum crisis and cyber city oedo 808
For more modern anime:
Sousou no Frieren/frieren the slayer as i mentioned before.
Wotaku ni koi
Tsukimichi ~Moonlit Fantasy~
Ergo Proxy (if you like mind screw anime, this borders on 00's but putting it here as it was revolutionary at the time)
Zetsuen no Tempest (another psychological story, though not in the same way as ergo proxy)
One Punch Man (you've probably seen it)
Stein's Gate
Tensei Shitara Ken Deshta
The Unwanted, Undead Adventurer/Nozumanu Fushi no boukensha (like frieren it's hard fantasy and i love every second of it)
The Irregular at Magic High School (this one i'm kinda hesitant to suggest as while i like it, it's not for everyone, it's probably something someone who liked the more famous anime would like though).
