I know this opinion borders on the sacreligious, but I think the Jane's Addiction cover of the Grateful Dead song "Ripple" on the 1991 benefit album Deadicated is better than the Dead's version on their highly country-flavored American Beauty.
Jane's Addiction bassist Eric A's comments on the song (from the Deadicated liner notes, Arista 1991):
This song meant a lot to me when I was too young (but trying) to grow facial hair, smoking too much pot and contemplating teen suicide. Before the glory of punk rock, I was a Grateful Dead fanatic, but don't tell anyone... it might be detrimental to my image.