Sorry, but I can't help but to correct two posts in this thread:
"Personal Jesus Depeche Mode (Johnny Cash original )" => it's the other way round, the song was written by DM's Martin Gore ("Violator" is one of the best pop albums of the 90s imo) and covered by Cash.
"Money's Too Tight to Mention By Reggie Watts (Originally by Simply Red)" => the Simply Red version is already a cover of a song by The Valentine Brothers, though I admit no one knows the original version.
Lots of great mentions in this thread.
There are many cover songs I like (e.g. I lately listened to Kate Bush's nice version of Marvin Gaye's Sexual Healing, where she gives the song her typical, charming twist), but very few are better than the original.
I agree though with Jeff Buckley's version of Hallelujah as my favourite one of the song ("Grace" is an incredible album) and especially with Johnny Cash's brilliant version of Trent Reznor's "Hurt", which is easily among the best cover versions I ever heard.
One that always stands out for me is Gram Parsons'/ The Flying Burrito Brothers' brilliant cover of the Jagger/Richards song "Wild Horses", which was actually released earlier than the Rolling Stones original. I actually like Parsons' version a bit more.
