Chan-wook's vengeance trilogy
http://www.imdb.com/title/tt0310775/ Sympathy for Mr Vengeance
http://www.imdb.com/title/tt0364569/ Oldboy
http://www.imdb.com/title/tt0451094/ Sympathy for Lady Vengeance

All Nolan films, my favorite being
http://www.imdb.com/title/tt0482571/ The Prestige

Leone classics
http://www.imdb.com/title/tt0060196/ The Good, the Bad and the Ugly
http://www.imdb.com/title/tt0064116/ Once Upon a Time in the West
http://www.imdb.com/title/tt0087843/ Once Upon a Time in America

Coen films, my favorite being
http://www.imdb.com/title/tt0100150/ Miller's Crossing

Scorsese, my favorite being
http://www.imdb.com/title/tt0112641/ Casino

Misc
http://www.imdb.com/title/tt0420223/ Stranger than Fiction
http://www.imdb.com/title/tt0780536/ In Bruges
http://www.imdb.com/title/tt0083658/ Blade Runner
http://www.imdb.com/title/tt0455957/ Goya's Ghosts

and one I cannot leave out
http://www.imdb.com/title/tt0088846/ Brazil

An underrated Japanese anime action movie: Redline

If you want to see romantic comedy redeem itself as a genre, watch A Serbian Film.

Fixed that for you.

You may have seen Scott Pilgrim vs. the World, which is a favorite of mine. If you haven't, I definitely recommend it as an action movie for a video game fan.

Robot Holocaust is a serious contender for the worst movie ever, which makes it practically worth seeing.

And I know that someone above specifically ruled out the recent UK Sherlock Holmes, but I liked season 1 a lot. Each episode is an hour and a half, so it's pretty movie-like.