A tricky and slightly controversial subject, some people love them, some think they verge on herecy-I can fall into either camp depending on the song and who's doing the cover.
Good as the original or better.
Reuben-The hand that feeds. Done on their "Rest Of" compilation " Should Have Gone To University" this is a really good cover of Trent Reznor's original. A cover of Gorillaz' Feel Good Inc. is also on this album, but it's not quite as successful as the NIN song.
Jeff Buckley/Led Zeppelin- When the Levee Breaks. This is so different from the original ( A happy go lucky Delta Blues classic) that it's almost a different song. Buckley's version is slightly superior for me simply because of his angelic voice. On a side note, A Perfect Circle do a dreamy Trip Hop version which is rather nice too.
Orgy - Blue Monday. A guitar heavy rocked up version of the new order classic. I like it a lot, but I can see people not really going for this one.
Deftones - Passenger. Not the Iggy Pop song or even the Elton John one, but a little known Duran Duran track and it's brilliant. Chino and the boys also do a great cover of Sade's No Ordinary Love too.
Worse than the Original/Shouldn't Have Bothered
Johnny Cash - Hurt/Rusty Cage. I know a lot of people like Cash's cover of Hurt, but for me it loses the desperation of Reznors' original-the feeling of a young man in the deepest pit of despair- And just doesn't work as well. His cover of Soundgardens' Rusty Cage sounds like something rejected from the Rawhide soundtrack. Fail.
Chris Cornell - Billy Jean. Oh god. If I thought Cash's cover of Hurt wasn't up to much, this abomination nearly made me fall off my chair. I wasn't a fan of the original, but this is, well, shit. No other words can describe it. The worst cover since Audioslave decided to ruin The Clash's "White Riot"
Glee. Fuck off.