As a general rule, I hate covers. But the following are quite good:
"All Along the Watchtower" Jimi Hendrix (original by Bob Dylan)
"Sweet Dreams" Marilyn Manson (original by Eurythmics) Actually I really like most of his covers, like "Personal Jesus" and "Tainted Love"
"Reconsider Me" Stevie Nicks
(original by Warren Zevon)
"Feel A Whole Lot Better" Tom Petty (original by The Byrds)
"Knockin' On Heaven's Door" Guns 'n' Roses (original by Bob Dylan)
"C'est la Vie (You Never Can Tell)" Bob Seger (original by Chuck Berry)
"Where Have All the Flowers Gone?" The Kingston Trio (original by Peter, Paul and Mary)
that's all I can think of at the moment.