Pandora is a free way to listen to music online, but not just ANY music. You create your own radio stations, you choose which music will actually be played on those stations, so if something comes up that makes your ears want to bleed, you can tell Pandora to stop playing it (and they will apologize, too).
For instance, I have about 10 different radio stations on there right now, anything from Gwen Stefani to George Winston to Kutless to John Denver. I'm always hearing music that I love, in addition to music that sounds much like the artist who the station is named for. Seriously, I listen to Pandora all the day long, and it's free, at least the commercial version with ads (however, I've yet to hear a commerical on Pandora and I've been using it for roughly three months).