My favorite, slightly satirical cover. Britney Spears 'Oops I Did It Again' covered by metal band Children Of Bodom.
http://youtu.be/K84j7CJIUKU
A cover of 'Wicked Game', originally by Chris Issac, covered by HIM. I prefer the original, but I find this cover interesting.
http://youtu.be/EsBQeZB3sIw
Another cover by HIM, original is Neil Diamond's 'Solitary Man'.
http://youtu.be/x-05M6zK56c
'Nothing Else Matters' by Metallica, covered by Apocalyptica. By far the most melodic, beautiful version of this song that has been done, and my favorite cover of all time.
http://youtu.be/rbTozgoj9OQ
Honourable mention, the long time favorite of many, 'I Love Rock'n'Roll'. Originally done by The Arrows, covered by Joan Jett to great success.
http://youtu.be/M3T_xeoGES8