I hate the Cash/Hurt cover. Just because it has deep "meaning" and background doesn't make it a good performance.
In general, I love covers. Everyone posting in this thread needs to subscribe to the podcast Coverville. 3x a week, about a half-hour each, all covers, tremendously put together.
For cover improvement, I'll have to go with the song "Metro" originally by Berlin. I couldn't stand it in the 80s as a teenager. However, System of a Down kicks it. Great stops, great chunkiness, and the intro is awesome.