Check out Shiny Toy Guns...they are recent but they have redone a few 80s songs, try this link...stripped, originally by depeche mode but i think this version is a lot better than the original even though i did see dp live perform it very well. You decide which is better??
One cover song that springs to mind is the song "Send Me An Angel" by Zeromancer. I've always loved the original song by Real Life, and it still holds up as a favorite 80's song for me. But since I've listened to Zeromancer's Industrial Rock cover of it more and more, I've grown to enjoy that version just as much as the original. Pretty cool considering I don't usually go for cover songs that often. Everyone here should already be familiar with the song. But for those who aren't here's both versions: