It's always great when you go to a concert  of your favorite band and they surprise  you with a memorable cover of a classic song. Here's a discussion about it. 

It's always a great treat when you see a show and the band goes into a cover but puts their spin on it . While I enjoy all types of music, I really like the Jam band community because they have made it part of their shtick and it works for them because the improvisation that happens in that kind of band always adds something to that cover.

I then have heard bands like Five Finger Death Punch and Disturbed almost create their popularity off covers that are really low tempo and dark, which for me is not my cup of tea because it's too depressing.

I really like the cover of Nine Inch Nail's Hurt by Eddie Vedder you can here it here.  Johnny Cash did it better though here.

Then there's Bob Dylan ...  Who wrote All Alone in the Watchtower and saw many memorable covers from it.  There's Jimi Hendrix's version, U2's version, and Dave Matthews version etc...

The point I'm driving at is that it's good to be spontaneous at concerts and develop you're own take on Classic songs... The thing to watch out though is if you're doing covers because you don't have any original material that's good ... Because that's a Cover band, and a lot of new artists today are proving themselves to be just that.