For on-line music I was a big fan of Pandora before the plug was pulled for European subscribers. I discovered a whole heap of new (to me) artists from the streamed recommendations that Pandora 'radio' played and loved the instant-mellow-evening-of music-old-and-new vibe that it excelled at. The ability to pick by genre, artist, suggestions or to be able to mix it up was (still is if you are in the U.S) unbelievably excellent!
Of late I've been using Last.Fm a bit but it feels like a pseudo Pandora and I haven't got into it in the same way, although it is really good.
But I've been playing big time with the new kid of the block, Spotify! I'm by no means an early-adopter, I've got into it at the same point as the entire blogosphere it seems, but nevertheless it warrants a mention especially if you've not given it a spin yet. You can do the genre radio stream, you can assemble play-lists BUT it's biggest plus is that whenever you are online it's like having access to the biggest i-pod (adopting Clarkson voice here) "In the world!"
The free version involves the ocassional advert but these tend to be for music it seems rather than the very cheesy, corny, 'singing' double-glazing-pitch beloved of l-o-c-a-l Raadiiio! Spotify also contains a wealth of artist info ... and the sound quality is spot-on.
What's not to love?
I'm currently listening to a whole heap of Natalie Merchant, her solo stuff and the entire 10,000 maniacs back catalogue, nice!
Very keen on Spotify, me. It's excellent if you want a comprehensive list of covers for a song, too.