Star Wars, Indiana Jones and Back to the Future:
There are six Star Wars films, four Indiana Jones movies and three Back to the Future movies.
They're all in American English and they're all a bit old, but they're all classics and just about everyone of my generation has seen them.
As someone who works in after school care, I can guarantee that Star Wars is still very popular with children as young as ten (they were literally born in 2004... doesn't that sound strange?) and from what I've heard they talk more about the events of the original trilogy than the new one.
The original first three Star Wars movies are now 4, 5 and 6. I suggest you start at 4.
I think only the first and the third Indiana Jones movies are well known by people my age.
Batman Trilogy (Batman Begins, The Dark Knight, The Dark Night Rises), Iron Man trilogy, X-Men trilogy, The Wolverine, Man of Steel, Thor, The Avengers etc.:
These are known more for their action than their plots, and they're all aimed at young adults. As far as I know they're all in American English (although a few have Australian or British actors playing the main protagonist).
The Lion King, Aladdin, The Santa Clause, Toy Story trilogy, Finding Nemo, The Incredibles:
These are all movies I loved when I was a child and I think you could still enjoy them as an adult.
I'm going to be honest, I googled 'Disney movies' to refresh my memory.
Pirates of the Caribbean trilogy:
This is really one trilogy and one spin-off.
The movies are in a mixture of British English and Pirate English.
The trilogy has good humour, good action and a great plot.