One recent cover that I really like is Metallica's cover of Deep Purple's "When a Blind Man Cries". I had never heard the song before I heard Metallica's version, so I went and sought out Deep Purple's original. I like both versions as each is a uniqie interpretation.
The thing about covers, is usually you know they are a cover song, and the band covering the song is offering its own interpretation of the original. I usually like covers if they're done well. One thing I really hate, and is one big reason why I can't stand rap music, is sampling. MC Hammer's U Can't Touch This wasn't a cover of Rick James, it sampled the original beat and bass line, and MC Hammer added his own lyrics. That's what I can't stand, sampling somebody else's music and trying to pass it off as your own.