I love disturbed's cover of "Shout"!!! Have you heard their new album yet? It's pretty good... different than "the Sickness", but it's good!
Powerman 5000 also did a cover of "Let the Good Times Roll" by the Cars.
David Bowie did a cover of Simple Minds "Don't you (forget about me)"
Save Ferris did a cover of a Dexies Midnight Runners song called "Come on Eileen"
Incubus did a cover of "No Scrubs", I think was originally done by Destiny's Child, but that's not 80's...
Biz Markee did a cover of "Benny & the Jets" by Elton John.
Shoot... If I was at home with my CD's (600+ of them), I could think of ALOT more...