I've (had) it fairly often that I was listening to a song, and out of the blue it turned out to be a cover instead of an original piece of music. To me there is nothing wrong with it. If the cover is, I can still immensly enjoy it even though it's not original from that artist. My dad makes fun of me now and then because of it, as I can't stand all music from what he liked back then, but whenever I listen to a cover of an older piece of music and I suddenly love it, he likes to mock me about it. Below three songs of which I like the cover better than its original.
Birdy - Skinny Love (Original by Bon Iver)
Lisa - Hallelujah (Original by Leonard Cohen)
Anberlin - Enjoy the Silence (Original by Depeche Mode)