Even as I grew up with the Robotech series and the imagery of other cartoons from Japan such as Battle of the Planets (aka Gatchaman) and Voltron (originally called Beast King GoLion and Armored Fleet Dairugger XV) Akira changed my sense of how much social commentary, plot and characterization could be embedded into a 'cartoon' even as admittedly, it is also one of the few films where I think it makes less and less sense the MORE I view it. But the imagery remains spectacular and evocative. It's a great, trippy story that laid critical groundwork for anime in the United States.
Robot Carnival was another personal favorite of mine for the sheer depth and variety of anime styles it hinted we could encounter. Fist Of The North Star was basically shoved down our throats during the early 1990s and its hyperviolence was a portent of the schlock to come that made it difficult to wade through much of the early anime offerings in the US with a focus on outrageous gore and melodrama with nonsensical plots. I'm probably particularly hard on Fist Of The North Star because I just can't get over the fact that I sit through 2 hours of searching for some character's sister, who then never once appears in the remainder of the movie after she's found. (!!!)
For my money, I deeply appreciate the depth and variety within the anime series, Cowboy Bebop, where, in addition to the progressive narrative, we found each episode exploring a different musical and literary theme/genre. One episode might look at the mythos of the cowboy western, another might be an homage to the world of Batman. It remains a classic series to me.
Another notable film I enjoyed was the re-envisioned Metropolis, that in recent years reminded me of the stunning, sweeping visionary heights Akira promised we were capable of. It diverges heavily from the Fritz Lang classic it's inspired by, but that in a way is what also makes it engaging, because it is faithful to many of the themes and motif's of Lang's opus.
A trailer for Lang's original work with a 1980s soundtrack for a restored 1984 version:
A standout series I continue to enjoy viewing was the retro Giant Robo series. Giant Robo was inspired by Mitsuteru Yokoyama's manga series and was an homage to Yokoyama's career.
The series featured great characters and plotlines from the manga artist's entire canon of work, effectively creating an all-new story. Set in the near future, ten years after the third energy revolution, you follows the master of Robo, Daisaku Kusama, and the Experts of Justice, an international police organization locked in battle with the Big Fire Group, a secret society bent on world domination. (aren't they all)
In 1999 I had the great fortune to be part of the Minneapolis Asian Children's Film Festival and to show a 10-film retrospective of the work of Hayao Miyazaki, from well-known classics like My Neighbor Totoro and Kiki's Delivery Service to Princess Mononoke, Nausicaa and the Valley of the Wind, Laputa: Castle In The Sky and many others.
All of them were great. But for personal reasons, my favorite is really always going to be Porco Rosso.
Porco Rosso is the story of an anti-fascist aviator transformed into an anthropomorphic pig in 1920s Italy. Porco is a bounty hunter who fights air pirates and an American soldier of fortune. The film is a fascinating meditation the tension between selfishness and duty, and ever an abstract self-portrait of Miyazaki himself.
But the long and the short of it is, while far from comprehensive, these would be among the first I'd recommend to others with an interest in manga and anime. And now you know! :)