Name the movies you personally allow to be canon in any chosen film series

[Me Myself and I]

Consider a series to be a collection of at least three directly connected films when it comes to the characters and/or story theme. Whatever you choose, no one can tell you differently.

If your list of accepted movies in a series, which you came up with for any reason, seems limited to some, so be it. The only consideration to add is that remakes stand apart as a separated series from the one(s) that came before it (i.e., Keaton and Bale Batman flicks).

I'll start. Anything left out I don't even think about or even acknowledge, let alone bother to re-watch compared to the other superior films in each respective series:

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The Terminator
Terminator 2: Judgment Day

Alien
Aliens

The Matrix

Batman Begins
The Dark Knight
The Dark Knight Rises

Batman (1989)

Star Wars: A New Hope
Star Wars: The Empire Strikes Back
Star Wars: Return of the Jedi

Raiders of the Lost Ark
Indiana Jones and the Last Crusade

Jurassic Park

The Lord of the Rings: The Fellowship of the Ring
The Lord of the Rings: The Two Towers
The Lord of the Rings: The Return of the King

Back to the Future