This Yglesias post on "authenticity" has developed into an interesting thread on rock cover versions. My own list of favorites, original artist in parentheses:
Pretenders, Stop Your Sobbing (The Kinks) Their first single, a great way to introduce the world to Chrissie Hynde's gorgeous vibrato.
Van Halen, You Really Got Me (The Kinks) Also their first single, and a great way to introduce the world to Edward's amazing guitar work, which I still totally geek out over.
Jeff Buckley, Hallelujah (Leonard Cohen) This version has probably been overplayed, but there's no denying either Buckley's astonishing voice or his facility with the lyric.
The Clash, Police and Thieves (Lee Perry and Junior Murvin) No comment required.
The Who, Summertime Blues (Eddie Cochran) Still rocks.
Frank Zappa, Whipping Post (The Allman Brothers) From an early '80s bootleg, with Bobby Martin on vocals. (What, you think Frank's taking that one?)
fIREHOSE, Sophisticated Bitch (Public Enemy) From their Live Totem Pole EP, which consists entirely of covers.
The Pixies, Head On (The Jesus and Mary Chain) One seminal alt-rock band covering another.
Dinosaur Jr, Just Like Heaven (The Cure) Likewise, but with that monster bridge and a J Mascis guitar solo that always makes me cry a little.