I'm surprised no one has mentioned Tarkovsky's clear influence on Terrence Malick's style. If you like anything by Malick, say, The Tree of Life or the most recent A Hidden Life, you should at least watch Mirror or Stalker.
Interesting— I like both but I wouldn’t think of Tarkovsky as having an influence on Malick. What would you say are the similarities, for you? Tarkovsky is intensely formal, seems blocked to the point of almost being choreographed, while Malick is quite the opposite in both regards.
I saw A Hidden Life within the last month and it is one of the best movies I have seen. I have also seen Stalker and after an interesting start it eventually bored me. I can see why you make the comparison, but I found them very different.