Spotify
There are several ways to listen to music on your PC. You could play a CD, or an MP3 from your hard drive - something I've been doing for over a decade. However it is increasingly common to stream music over the internet, via one of literally thousands of radio streams. While you have access to a greater choice of music/genres than you can ever possibly hope to own yourself, you are limited by what the particular station chooses to play at that point in time. Things changed with Pandora.com (now limited to US residents only) which allowed you to enter a song or artist, which generated you a playlist of similar songs to listen to. But you still did not have a free choice over the exact music you heard.
Enter Spotify. I stumbled upon this gem a little late in the game, but I've jumped on board the bandwagon and I'm behind it all the way. Spotify is a downloadable client for Windows or Mac (or Linux via Wine) which allows you to search for songs or artists and generate your own playlists. This is not another example of Pandora, or a radio station - you have the power to choose exactly what song/artist/album you listen to.
This would all be for nothing if the library of songs was small, but I have found it to contain a huge diverse range of tracks, even some obscure Portuguese bands Cat listens to. And Spotify add thousands of new tracks each week - they even post a document on their blog with all the new additions! On top of that, all the music is in high quality OGG Vorbis format - much better than your standard MP3 - and plays flawlessly over broadband. I've never had it buffer or stop during a song, not even once. Just high quality music of your choice played when you want it, without interruption.
Well kind of... 
The truth is, you will receive an advert every once in a while, just like a commercial radio station. However they are few and far between (I have listened on occasions for a few hours before receiving an advert, sometimes it can be as often as every 30 minutes). However the ads are unobtrusive and short, and far far less than you would hear on a normal radio.
To top this all off, it's available in the UK and it's free. There are pay for options which cut out all the adverts for £9.99 a month. The truth is, it's not worth paying for. The ad supported version is superb. And free-er 
I seriously recommend this to anyone looking for a legal way to listen to a huge library of music and doesn't want to have to buy the tracks. All you need is a computer, a broadband connection and a good set of ears
Check it out at www.spotify.com