There are a lot, I mean a lot of bad cover songs out there. It pains me to hear a lot of them, they're a waste of time and creative energy. However, sometimes the musicians do it right, and then it is a nice tribute to a former glory song, as well as an ingenious creative output from the newer artist themselves. Here is a short list of some cover songs that have gone over quite well, in my opinion.
Ziggy Marley - Drive (from the Cars)
Radiohead - Wish You Were Here (from Pink Floyd)
Smashing Pumpkins - Landslide (from Fleetwood Mac)
Fiona Apple - Across the Universe (from the Beatles)
Cat Power - Sea of Love
Lauryn Hill - Can't take My Eyes off of You
Listen, and enjoy.