If you're in North America, or maybe only the USA itself, you should try Pandora.com, one of the coolest sites to come out of "web 2.0" a couple years ago. Unlike Last.fm, they aren't run by a label and so don't have a label's agenda at their core.
Plugging in a couple artists or songs, and then making a few thumbs-up or thumbs-down recommendations based on their choices, you'll soon be hearing music you've never heard of before, and wondering why. There are links to purchase on Amazon and iTunes.
I've not been able to log in there since the various labels made Pandora shut off access to foreign-to-America IP addresses in 2007, but I've just been able to log in and am finally able to access my old favorites! Woot! Still no music access though. It's hard to believe the labels can be so utterly stupid and shortsighted as to go out of their way to block an agency which helps people find their music, and provide an easy and legal means of purchase. Just mind blowing.