My two favorite ways to find new music is reading Filter Magazine (those guys are the closest in the mag world to my taste in music), and I have a Rhapsody subscription.
I love Rhapsody so much. When I first got it, it was like Christmas only better. You can listen to almost anything as many times as you want all the way through. I really like the fact that when I find a new band I like, I can listen to their entire catalogue and hear their older albums. I spent a whole day listening to Bowie in chronological order once. I also did that with Pink Floyd once.
The best way to stumble on new stuff through Rhapsody though is that they have a "build your own radio station" type of thing. The way that works is you put in 10 bands that you like, and it will play stuff by those bands, plus other bands that are similar that you may or may not have heard of. That's how I found Camera Obscura and Clem Snide. It's a lot of fun.