I was never a fan of "Hurt," the original version. It's, as you say, the very epitome of emo, and not nearly as fun as other NIN songs that are equally (if not more) emo. What Johnny Cash's version brings to it is the weight of age and pain in his singing. Trent Reznor singing it is a young dude whining about one problem on his otherwise still very open-ended, probably-going-to-get-better life. Johnny Cash singing it is filled with the remorse of a long life lived unhappily, full of remorse and pain.

Okay, so it's still emo, but it has some weight to it. I love it.