This ain't a list for best anime ever but of those anime which influenced other anime.
The Top Ten
1Dragon Ball ZDragon Ball Z is a Japanese anime television series produced by Toei Animation. Dragon Ball Z follows the adventures of Goku who, along with the Z Warriors, defends the Earth against evil. The action adventures are entertaining and reinforce the concept of good versus evil. Dragon Ball Z teaches valuable ...read more.
Series that introduced anime to the world and inspired all major anime
The granddaddy of all anime. Without Dragon Ball Z, anime wouldn't be where it is today. Enough said. - ModernSpongeBobSucks
Of course. Dragon Ball Z has revolutionized the whole shonen genre. - Goku02
2Neon Genesis EvangelionNeon Genesis Evangelion, commonly referred to as Evangelion or Eva, is a Japanese animated television series produced by Gainax and Tatsunoko Production, and directed by Hideaki Anno.
3Cowboy BebopCowboy Bebop is a 1998 anime television series animated by Sunrise featuring a production team led by director Shinichirō Watanabe, screenwriter Keiko Nobumoto, character designer Toshihiro Kawamoto, mechanical designer Kimitoshi Yamane, and composer Yoko Kanno.
I legit know a person who was a lot like Edward at the age of 13.
When this is the anime that everyone uses on Greatest Anime of All Time to bash other anime series like Dragon Ball Z, Naruto, One Piece, Bleach, Fairy Tail, Sword Art Online, and Pokemon, you know Cowboy Bebop has cemented itself as one of the most influential anime ever. - ModernSpongeBobSucks
4Astro BoyAstro Boy, known in Japan by its original name Mighty Atom, is a Japanese manga series written and illustrated by Osamu Tezuka. It was serialized in Weekly Shonen Magazine from 1952 to 1968. The original 112 chapters were collected into 23 tankōbon volumes by Kodansha.
It influenced DBZ enough said. - Goku02
5Fullmetal AlchemistFullmetal Alchemist is an anime series adapted from the manga of the same name by Hiromu Arakawa. It is about two brothers, Edward Elric and Alphonse Elric, trying to restore their bodies after failing at bringing their mother back to life. It aired in 2003 and was remade as Full Metal Alchemist Brotherhood ...read more.
6Death NoteDeath Note is a Japanese television drama series based on the manga series of the same name by Tsugumi Ohba and Takeshi Obata.
The show is centered around Light Yagami a promising highschooler and aspiring detective with a strong sense of "justice".
This paved the for DBZ, Sailormore and pretty much most of the rest of this on the list. This anime single handedly popularized amine for the rest of the world.
8Ghost in the Shell
9Mobile Suit Gundam
10Samurai ChamplooSamurai Champloo is a Japanese anime series developed by Manglobe. Samurai Champloo is set in an alternate version of Edo-era Japan with an anachronistic, predominantly hip hop, setting. It follows Mugen, an impudent and freedom-loving vagrant swordsman; Jin, a composed and stoic rōnin; and Fuu, a ...read more.
12One PieceOne Piece is a manga franchise created by Eiichiro Oda. The manga has been adapted into an original video animation (OVA) produced by Production I.G in 1998, and an anime series produced by Toei Animation, which began broadcasting in Japan in 1999 and has aired 851 episodes to date.
13Sailor MoonSailor Moon is a Japanese shōjo manga series by Naoko Takeuchi. It was originally serialized in Nakayoshi from 1991 to 1997; the 52 individual chapters were published in 18 tankōbon volumes. ...read more.
16BleachBleach is a Japanese anime series based on Tite Kubo's manga of the same name. Bleach adapts the first 54 volumes of Tite Kubo's manga series of the same name. In addition, 4 anime-original arcs were broadcast in-between and during the adaptations of original arcs of the manga. ...read more.
17NarutoNaruto is an anime and manga franchise Naruto, created by Masashi Kishimoto. The manga was later adapted into a television anime, which was produced by Studio Pierrot and Aniplex. It premiered across Japan on the terrestrial TV Tokyo and other TX Network stations on October 3, 2002. The first series ...read more.
19Ghost in the Shell: Stand Alone ComplexGhost in the Shell: Stand Alone Complex is an anime television series produced by Production I.G and based on Masamune Shirow's manga Ghost in the Shell.
20Jojo's Bizarre AdventureJojo's Bizarre Adventure is an anime and manga franchise originally written by Hirohiko Araki. It centers around the perilous journey of the members of the legendary Joestar bloodline.
21PokemonPokémon, abbreviated from the Japanese title of Pocket Monsters and currently advertised in English as Pokémon: The Series, is a Japanese anime television series, which has been adapted for the international television markets.
22Fist of the North Star
23MushishiMushishi is a manga series written and illustrated by Yuki Urushibara. It was serialized in Afternoon Seasons Zōkan from 1999 to 2002, and in Monthly Afternoon from December 2002 to August 2008. The individual chapters were collected and released into ten tankōbon volumes by Kodansha.
25The Melancholy of Haruhi Suzumiya
26Fate/Stay NightFate/stay night is a Japanese visual novel and anime series by Type-Moon. There are three story lines in the visual novel: Fate, Unlimited Blade Works, and Heaven's Feel. A 24-episode anime series based on the Fate route and a film based on the Unlimited Blade Works route were made by Studio Deen. A ...read more.
27Gurren LagannGurren Lagann, known in Japan as Tengen Toppa Gurren Lagann, is an anime series animated by Gainax and co-produced by Aniplex and Konami. It was also directed by Hiroyuki Imaishi and written by veteran playwright Kazuki Nakashima.
28Fullmetal Alchemist: BrotherhoodFullmetal Alchemist: Brotherhood is an anime series adapted from the Fullmetal Alchemist manga by Hiromu Arakawa.
29Science Ninja Team Gatchaman
30Phoenix WrightPhoenix Wright, known as Ryūichi Naruhodō in the original Japanese-language versions, is a fictional defense attorney in Capcom's Ace Attorney video game series.
31Dangan RonpaDanganronpa: The Animation is a 2013 anime television series based on Spike Chunsoft's murder mystery video game, Danganronpa: Trigger Happy Havoc.
32Dancouga – Super Beast Machine God
33Cardcaptor SakuraCardcaptor Sakura, abbreviated as CCS and also known as Cardcaptors, is a Japanese shōjo manga series written and illustrated by the manga group Clamp.
34Revolutionary Girl Utena
35Magical Girl Lyrical NanohaMagical Girl Lyrical Nanoha is a Japanese anime television series directed by Akiyuki Shinbo, with screenplay written by Masaki Tsuzuki, and produced by Seven Arcs.
36The King of Braves GaoGaiGar
37Shakugan no Shana
38Puella Magi Madoka MagicaPuella Magi Madoka Magica is a 2011 Japanese anime television series produced by Shaft and Aniplex, directed by Akiyuki Shinbo, written by Gen Urobuchi, music by Yuki Kajiura, opening sang by ClariS, ending by Kalafina (sometimes by the seiyuus) and original characters by Ume Aoki. It also has 3 movies, ...read more.