I know what your thinking, and no, that's not the name of my latest story.
I've heard about the web music app Pandora for a long time, but never checked it out. Recently I remembered it and pulled it up. Going to the website presents a front end that lets you specify an artist (or a song) that you like, and Pandora starts playing something by that artist.
Pandora builds a queue of music based off of your initial selection and the Music Genome Project. Basically, it analyzes your selection and assigns the song certain attributes that it matches against songs in its database. Subsequent songs are automatically queued up and played.
I've started with various musicians I like and also tried some obscure ones. The vast majority of times I've enjoyed what I've heard, with some obvious matching selections but also some bands that are new to me. It's great for parties or just hanging around if you are tired of your current media selection or don't want to create a custom playlist (or are too lazy to hit Shuffle).
There is also a Pandora app for mobile devices, but I'm not sure how great this is due to it always being on and streaming data/music. I could see your battery draining due to the Pandora app, but as I don't have a phone with that kind of capability I'm basically talking out of my Napster. I'm sure it works - why offer it otherwise.