Inspired by this post, remember the definition of “seminal” when answering. Think of it (as it was in the original post) as The Great Gatsby was to books in the 1920s as X was to offensive/defensive schemes in Y.
Here are my picks. Add your own:
1900s – 1910s: Single-wing.
1920s: Notre Dame Box.
1930s: I’d like to choose the TCU/Dutch Meyer/Sammy Baugh spread offense but I’m not sure this counts as seminal. I leave this one for the readers.
1940s: T formation.
1950s: “Pro-style” offensive schemes of Paul Brown (Cleveland Browns), Weeb Ewbank (Baltimore Colts), and Vince Lombardi (Packers), and the 4-3 defense developed by, among others, Tom Landry as defensive coordinator of the New York Giants. Almost everything in the current NFL is merely a footnote to the 1950s.