Evidence - Faith No More.  The definitive FNM song.  Smoothed out yet progressive and frantic in it's own way.  The strings aren't cheesy and the funk isn't forced.  Hell, this song is THE best R&B funky progressive jam ever written.

Hurt - Johnny Cash.  The best cover song every done by anyone in the history of forever.  It would be an injustice to describe the emotion here.  It is all encompassing, everything a person can be or feel is in this song.  

Live With Me - Massive Attack.  Another soulful, desperate song.  It's so much more than the trip hop shit Massive Attack is known for.  Layered and full, unlike most of their remix work.

Zombie - The Cranberries.  It's taken the better part of two decades but I'm ready to admit liking her voice.  May have to seek out some of their newer stuff if it exists.

Body Talk - Ratt.  For my money, they're the best of the 80's "hair bands".  This song is a half step below thrash with a really poppy chorus and a fun bridge.  Warren is a superb soloist.