let me chime in with some true classics, most are very old school.
Girls Und Panzer (12 eps, 6 short OVAs (~10 mins. ea), 1 log OVA (~37 min), and a 90 minute movie.
2012: High school sports drama where the most feminine of sports is TANK COMBAT in WW2 replicas. fairly new, but done in an older style (and the premise is CRAZY AWESOME)
Bubblegum Crisis - 8 ~1 hr OVAs (1987-91), Old school classic. Cyberpunk by way of Iron Man. 4 Mercenaries in power armor vs a gigantic megacorp. Had a late 90s remake, Bubblegum Crisis 2040. Both on Hulu
Ranma 1/2: (1989-93): another old-school classic. Martial Arts comedy of gender. Ranma Saotome and his Dad Genma went on a martial arts training trip to china, and fell in to magical pools where creatures drowned: Genma turns into a Panda. Ranma turns into a GIRL. If that wasn't enough, his deadbeat dad has betrothed ranma to MULTIPLE potential Fiances, all of whom are also master martial artists.
Tenchi Muyo: 3 OVA series and 2 TV series. and several spin offs, some of whivh remap the characters into different situations, The OVAs and EACH TV series is a slightly different continuity. One of the great Toonami shows of the 1990s, and probably the definitive Harem anime (where a bunch of interesting female characters are attracted to a cypher-like male that audiences can project themselves onto)
Yamato 2199: 2011 remake of 1974's Space Battleship Yamato. Space Opera at its finest. They updated the Animation level to modern film-quality, and added more female characters, but the basic plot is the same from 1974. In the year 2199, Earth is losing a war with the interstellar Gamalan Empire. The surface of the earth has been bombed to uninhabitable radiation levels, and the survivors of humanity dwell in underground cities. for two years, after getting a message from Starsha of Isadar, Humanity has been buildng a last desperate hope, now ready..but the radiation levels are creeping down toward the cities. Only 1 year is left to humanity. The IJN Yamato has been rebuilt as that last desperate starship, and it has 1 year (365 days) to travel from earth to Iscandar in the Lesser Magellanic cloud, 144,000 light years away, and back, in their way is the entire Gamalas Navy.
Record of Lodoss War, An OVA series (1990-92) and 26 episode tv series (1996), they split continuity about OVA episode 7 or 8. one of the best examples of cross-cultural osmosis for integrating all the best known Western fantasy tropes in an anime. Its actually based on the author's 1979-81 college D&D game!
K-On! and K-On!! (2009-10), Cute girls form a band and do cute things.
Nausicaa Of The Valley Of The Wind (1984), Kiki's Delivery Service (1989), Princess Mononoke (1998), Spirited Away (2001): the greatest films by Japan's greatest anime director, Hayao Miyazaki.
Lupin III: The Castle of Cagliostro (1979): the first, and most influential of the Lupin films, of which there is now one every year. Lupin is a lovable thief who tends to do the impossible with his gang: crack shot Jigen, Samurai Goemon, and femme fatale Fujiko, always pursued by Tokyo Police Detective Inspector Zenigata. This has Lupin infiltrating a massive counterfeiting ring
Project A-Ko (1986): hilarious parody of all 1980s anime.
AKIRA (1988): ultra violent cyberpunk/psionic anime film. in post-apocalyptic Neo-Tokyo, a bike ganger gains psychic powers he can barely control
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