I love listening to covers--one band's interpretation of another artist's songs. Here's an earlier entry spotlighting some cool ones.
I think I have enough new ones to do another post, but most of the links come from youtube. You may find MP3's of these on music blogs, so Elbows is your friend. (By the way, as far as I know, downloading from most music blogs is legal. but I am not a lawyer, so don't sue me.)
One of the cheesiest songs of all time is "I've got you babe", originally by Sonny & Cher. Some dude named Aidan Moffat has covered it very well.
Speaking of cheesy songs, Shawn Mullins (the guy who did lullaby) has covered Wham's Wake me up before you go go.
I really like what I've heard of The Editors so far (admittedly not all that much, but I especially like Smokers), but their cover of Road to Nowhere (Talking Heads) is pretty cool.
These days, John Mayer seems to be everywhere, probably because he released an album. His cover versions of Message in a Bottle (The Police) and Free Falling (Tom Petty) are so good that hipsters think that these are really his songs.
Anything Jack White and company does is sure to be cool, but the White Stripes version of Jolene (Dolly Parton) is awesome.
I love Tori Amos' voice; her version of Losing my Religion (R.E.M.) is haunting because of it.
Last one: if you've ever watched an episode of Cold Case, there's a 90% chance you've heard REO Speedwagon's song Keep on Loving You. Lisa Loeb & Dweezil Zappa cover it here.