Some of these versions aren't really noteworthy except to help the exceptions stand out. Original Blue Öyster Cult, from Agents of Fortune, 1976. This is the longer album version, not the radio edit.
Goo Goo Dolls (punk). Their 1987 eponymous album. Nothing new here, just a sped-up, punked-out style.
Gus Black (rock), 1996 from the Scream soundtrack. Very slow. Very somnolent. This one puts me to sleep.
HIM (metal, Finland), from Greatest Love Songs Vol. 666, 1997. Nice version this time. I like the heavy style and the female vocals.
Big Country (pop/rock, Scotland), from Undercover (an album of only cover versions), 2001. This is Big Country with their replacement lead singer after their original (Stuart Adamson) died. Not the same singer as on "In a Big Country" of 80s pop fame. I like Big Country, but this version isn't remarkable either. Mostly just an imitation of the original.
Unto Ashes (neo-medieval/darkwave), from Empty Into White, 2003. Of the covers, this is my favorite, with its dreamy, phantasmic atmosphere.
Wolf (Sweden, metal), from Evil Star, 2008. Nothing new to see here, either. In my opinion, Sweden (as well as Finland) has turned out some awesome doom metal bands, but this is just more generic heavy metal with high male vocals and this version doesn't really do anything new. They even keep that arpeggiated guitar break in the middle of the song.
Sever Your Ties (rock), from Safety in the Sea, 2008. There's really nothing new here, either, but I like this one better than the Wolf version, for some reason. There seems to be a greater sense of urgency in it.
Candlemass (Sweden, doom metal), from Don't Fear the Reaper (EP), 2010. As I was saying: Swedish doom metal, and Candlemass are among the best. Another of my favorites. I like the very slowed-down, heavy, almost ponderous tread of this one. Also, this is melodic doom metal, which means they actually sing and have vocal harmonies instead of just growling.
L.A. Guns, from Covered in Guns (another album of only covers), 2010. Pretty much a carbon-copy on this one.
So to recap, my favorites of the covers are:
1. Unto Ashes
There may well be others that I'm unaware of. And as I've said before, when it comes to these covers I'm interested only in the ones that made it to some kind of recorded medium; lousy camcorder recordings from some concert somewhere that you've posted on YouTube don't count. I'm aware, for example, that both Evanescence and R.E.M. have performed this in concert, but the videos I've seen have terrible audio and let's face it: the R.E.M. attempt is just sad and ugly.