Radio online.
Here follow a few links to onine radio stations or musical services. They all feature a free (as in gratis) version of some kind, although they may (a) require resgistration and the creation of a user account and/or (b) offer mo' better features if you pay a fee.
Musicovery present us with a remote where we can choose genre, mood, a decade, etc. Then, an interface worthy of Timothy Leary conducting one of his psychotropic experiments will select a song that meets the selected criteria and is connected through multicoloured tendrils to other tunes that have some sort of similarity. We can browse through those, let the service choose the next one for us or play once again with the remote. Entertaining.
Last.fm is a CBS owned online radio station and music recommendation system that builds users' profiles and statistics based on their musical tastes. There is a Wikipedia article detailing its features and how it works.
Pandora is a music recommendation system and internet radio service created by The Music Genome Project. Users enter a song or artist of their liking, and the service responds by playing selections that are musically similar. Users can also provide feedback on the individual song choices, which Pandora takes into account for future selections. ( SW Note: at the time of writing, Pandora only works in the US due to licensing problems. Pity. )
[ Text taken (with minute edits) from the Wikipedia article on Pandora. ]