Probably someone has made this point before, but it occurred to me a while back that you can better appreciate both a cover of a song and the original by reversing them: that is, listening to the cover as though it were the original and the original as though it were the cover. This works great for

• "Friday I'm in Love" — which Yo La Tengo first performed and was later covered by The Cure;
• "Take Me to the River" — who would've imagined that Al Green would cover a Talking Heads song?
• "All Along the Watchtower" — Hendrix's original is iconic, but Dylan's reimagining of it as a spooky mostly-acoustic mid-tempo number is pure genius.