Here are some of the best music sites I have come across. These are excellent for either discovering new music or playing music without having to download it first.
Music Jukeboxes
The following two sites enable you to search for a particular artist and play all his songs, or even make up your own radio station using selected tracks, among other features.
Custom radio stations
These sites on the other hand, promote the very interesting and useful concept of creating radio stations based on your tastes. For example if I type in ‘Gigi D’Agostino’ they will play some music from Gigi as well as music from other similar artists. These sites are very good for discovering new music as they record your tastes and try to match them, quite succesfully I must say.
- www.last.fm
- www.jango.com
- www.pandora.com (only available for US citizens)
So happy listening! If you come across any other similar sites leave a comment and I will update this list 
Web professional in Malta, Europe. Focusing on building visually stunning websites that are easy to maintain, usually using WordPress as the CMS. Web developing since 1995, loving WordPress for more than 5 years.