I think Terminator 2 is one of the best examples. A film where you feel the protagonist is in constant danger for the whole movie. I think the sci-fi genre lends itself well to this type of movie as the unrelenting force trying to kill the hero can be made out to be unstoppable and far scarier than any human.
What other films do you think fit this description? Im struggling to think of good ones without sci-fi elements.