Much of the music I listen to is from the 60s, and many bands back then covered each others' songs. If done well, I enjoy hearing a different interpretation of a song.. if its a good song to begin with.
Bob Dylan was a great songwriter, but he doesn't have much of a voice, epecially when he's wasted. The Dead do Dylan better than Dylan does. The Dead also used to do terrific drawn-out improvisations of the Stones' Satisfaction and a coupla Beatles tunes too, such as Dear Prudence, Rain, Hey Jude and LSD. They also did nice improvs of Traffic's Dear Mr. Fantasy. Hell, the Dead covered just about everyone.
Many people have done great covers of Take Me To The River, including the Dead, Talking Heads and Eva Cassidy.
I typically like covers, when done by people I like. That only makes sense though, right?
Janis Joplin and the Dead both did a good job in Chris Kristofferson's Me And Booby McGee.
CSN&Y did a good job on Joni Mitchell's Woodstock, too.