I recommend you Pandora: It is probably the best service online to help you discover music based on your current tastes.

With Pandora all is simple : Just name an artist or a song and it will instantly generate a streaming radio in the “feel” of that artist. You can play in your browser without any download. The sound quality is amazing, the relevancy of exploration results is also great (although limited if you are an expert in music, limited also is classic music). The user interface is simple, easy and fast.