Well if Dready's in, I'm in. Good call on pointing out Abram's "Star Trek".
Movies like die hard , the A team and Salt have lots of explosions, a decent script with little twists and turns and a lot of remember able punch lines. But then there r others like the Matrix which arent like your average action movies, cause they deal with a wide range of themes another example i think would be the transformers ...
"A-Team" was a fun movie. The openning bit, with the dogs, and all that, just plain fun Summer Blockbuster Popcorn Flick, and it held that energy for the duration of the movie. However, I understand and agree with why you left it off your list of "Movies which where more than action Movies". That's because it doesn't have a story. Not one that pulls the audience in, anyway. Also, I should mention that I was super, super stoned when I saw it.
The list of action movies that are more than action movies is long -- too long to even try and cover here. Because most of them, like Dready pointed out, aren't action movies. "The Matrix" is a brilliant sci-fi. It also happens to have some badass action. "The Bourne Identity" is the best spy-thriller ever made (in my opinion). It also happens to have kickass action. "The Fugitive" is the best blah, blah, blah, you get my point.
What all of these movies have in common, no matter what genre you want to categorize them in, is
story. A successful film has a story that grabs you and won't let go, and that's just as true for action films as any other genre.