I will just throw out the classics that I think are must see’s. All of the below heavily influenced the genre.
Speed Racer 1967 series (changed animation in America in the next decade)
Mobile Suit Gundam 1979 (kicked off the transforming robot crazy) Yes, there were transforming robots in the 1930s…did not kick off the transformers though like this did.
Grave of the Fireflies (arguably the greatest anime ever made) dont get mad at me if you cry by the end. Very powerful story, very moving.
Original Fist of the North Star 1986 (made Anime + blood/gore mainstream)
Akira…do I need to say why?
Original 13 part Record of Lodoss War from the early 90s (First D&D style anime fantasy)
1997 Bastard series
Full Metal Alchemist: Brotherhood. Make sure its Brotherhood. Amazing story.
Death Note 2006 series