Off the top of my head, some covers I enjoy...
"Electric Eye" The Mother Truckers (original by Judas Priest)
"Play it All Night Long" Drive-By Truckers (original by Warren Zevon)
"Never Turn Your Back on Mother Earth" Martin Gore (original by Sparks)
"Never Turn Your Back on Mother Earth" Neko Case (original by Sparks)
"Over Under Sideways Down" The 77s (original by The Yardbirds)
"Running Up That Hill" Placebo (original by Kate Bush)
"Renaissance Man" The Ocean Blue (original by The 77s)
"Shotgun Angel" The 77s (original by Daniel Amos)
"Wild Horses" The Sundays (original by The Rolling Stones)
"Helter Skelter" U2 (original by The Beatles)
"Across the Universe" Fiona Apple (original by The Beatles)
"Dead Souls" Nine Inch Nails (original by Joy Division)
"Molly's Lips" Nirvana (original by The Vaselines)
On a fast train nowhere, but we're not there yet.