I actually prefer the lesser known and hard to find version of "Hurt" by Peter Murphy (lead singer of Bauhaus...Bauhaus later went on to form Love and Rockets without Mr. Murphy).
Nirvana's remake of D-7, Return of the Rat (originally by the Wipers, great band, Is It Real? is one of the best albums ever), and Jesus Doesn't Want Me For A Sunbeam.
Sex Pistols "Roadrunner" over The Modern Lovers original (mostly because Rotten is pissed off cause he can't remember the lyrics to it).
Sex Pistols "No Fun" over The Stooges original.
Roy Orbison's "Love Hurts" is MUCH better (IMHO) then the Everly Brothers, Jim Capaldi's or Nazareth's.
Classical music's best cover is La Campanella (Liszt), which sounds much better than Paganini's original.
I have to go with leavingwt, never heard a cover of the Beatles that sounded even half as good.
Never heard a cover of Elvis Presley that sounded close to good.
Pearl Jam's Last Kiss sucks compared to the original by Wayne Cochran, but I like J. Frank Wilson and the Caviliers version the best out of the tons of people who have covered that song.