Here's a few single song covers I like:
Van Halen - "Oh Pretty Woman"
Guns N Roses' - "Knockin' On Heaven's Door"
Aretha - "Let it Be" -
https://www.youtube.com/watch?v=4Y8f-7U9G1g
U2 - "Helter Skelter" - "Charles Manson stole this song from the Beatles - we're stealing it back..."
Springsteen - "Jersey Girl" - too many of the young'uns don't know about Tom Waits... (and of course the Detroit Medley goes without sayin' but I'm sayin it anyway...)
Johnny Cash - "Hurt" (no doubt the best of his covers working with Rick Rubin; beware of "Danny Boy" - ick)
And there were a few albums full of covers that introduced me to several singer-songwriters in addition to the legends:
Nanci Griffith - "Other Voices, Other Rooms" - featuring "Tecumseh Valley", "Speed of the Sound of Loneliness", "Boots of Spanish Leather"
k.d. lang - "Hymns of the 49th Parallel" - "Helpless", "Hallelujah", "Bird On A Wire"
Shawn Colvin - "Cover Girl" - "Heart of Saturday Night" (Waits), "Someday" (Steve Earle), "If These Walls Could Speak" (Jimmy Webb)