........if there's a website when I can listen to any song of my choice free? I don't want to download music, just choose a song and hear it. Does such a website exist?
allofmp3.com and most other download sites allow you to listen to 30 secs of tracks for free. MSN Music allows you to listen to whole tracks for one penny per track.
Yes you pay by credit card and you then have a credit balance which is reduced every time you listen (or purchase by downloading). You can credit quite small amounts. I listen to albums on MSN and purchase from allofmp3 which is a very cheap Russian site but excellent quality and an extremely comprehensive catologue. Again you have to buy credit in advance. I have not had any problems.