There are countless options for customizable internet radio, with heavy hitters such as Spotify or Pandora. All of them allow for creating stations based off of genres, artists, albums, or songs. They also proclaim features such as the ability to learn your tastes from your feedback in order to tailor a "station" to you, making it all the more personal.
Here's where they all fall short... They don't exactly listen when you say you don't like something. There are times you vote down a song and yet the same song will play again in the future. They also fail to extrapolate from certain choices. For example, if I'm listening to 70s rock, and you were dumb enough to include ABBA, I'm going to downvote it. It doesn't belong. Don't play the same song again in the future. and if you play a different ABBA song, I'm going to downvote that too. At this point, you should start to make the prediction that on my personalized 70s rock station, I don't ever want to hear ABBA.
Along with that, the best feature I think you implement and make available to users is a "Don't play anything by this artist" option. If you were to go that far, allowing more granular settings such as dates would be great too. Sure I'm willing to trust you on "Greatest Hits of the 90s!", but when I'm listening to "Jazz Classics" I couldn't be farther from trusting you. Don't play me Wynton Marsalis. Don't you even think about playing Chris Botti. And you better not think about playing anything past the 60s. Even that could be argued as beyond classic. You know what, you should probably just let me enter those specific date ranges. Then we'll all be happier. I'll be more inclined to give you my money for your premium service, because you give me a truly personalized experience, and you'll have less complaining from me.