Lucky Star and K-on for CGDCT
Evangelion for meta-commentary and deconstruction, to the point that future works that qualify often get called the “Evangelion of <genre>”
Fullmetal Alchemist Brotherhood and Attack on Titan for battle shounen
Bocchi the Rock for girls band anime, specifically
Lupin III: The Castle of Cagliostro for pretty much all of Ghibli
Akira for 90s anime
Astro Boy (Tetsuwan Atom). Basically defined and kick-started anime as a genre and aesthetic. If there’s a most influential anime, it’s this.
Or maybe Space Battleship Yamato. It turned anime from “TV comics” into, well, anime.
Mazinger Z. Pioneered the giant mecha anime. Also Getter Robo.
Science Ninja Team Gatchaman (better known in the West for its adaptation as Battle of the Planets). The template for the super sentai team genre.
Mobile Suit Gundam. Revolutionised the giant mecha genre moving from simple good vs. evil children cartoons to complex geopolitical narratives. Also, in a similar vein, Macross.
Urusei Yatsura. The template for moe anime. See also Ranma ½.
Nausicaä Of The Valley Of The Wind. The foundation for Studio Ghibli’s aesthetic, tone, and narrative.
Akira, Dragon Ball, Cowboy Bebop. Brought anime to the mainstream in the West, and Dragon Ball is a cornerstone of the shounen genre, with probably only One Piece coming close in influence.
Sailor Moon. Not the first magical girl anime by a long shot, but arguably the cornerstone of the genre. Also Puella Magi Madoka Magica, which redefined and revitalised it.
Neon Genesis Evangelion, already mentioned in the OP. Extremely influential in the 90s and noughties.
Ghost in the Shell. Took over from Akira as a cornerstone of cyberpunk anime.
And I’m surely missing dozens, I’m far from an expert in the genre.
Personally Space Pirate Captain Harlock, Doctor Slump, Dragon Ball, Urusei Yatsura, and Ranma ½, and later Akira, My Neighbour Totoro, Nausicaä, Ghost in The Shell, and Fullmetal Alchemist were my main introductions to the genre (besides stuff that was in the background but I didn’t really follow or, at the time, recognise as a specific genre), but that’s just personal history and preference; I tried to list ones that seem to objectively have had significant influence on the genre or industry.