The leading (i.e. most popular) format for downloading & playing music is, by far, MP3. (See the de facto standard shareware MP3 player.) Other contenders are Real Player, Liquid Music Player,.
MP3, however, has a large head start.
Most MP3 music is available for free.
A lot of it is by struggling artists unknown to the general public who haven't been able to land a major studio recording contract (with all the publicity and support that implies).
Where can you find MP3 music files? Try Lycos' new MP3 search engine.
There are also claims that a lot of MP3 music is copyrighted and therefore pirated, as well.
MP3 is digital music. How can you prevent people from downloading copyrighted bits and bytes?
The recording industry has come up with their own plan, the Secure Digital Music Initiative.
The general idea is to protect both copyright (and artist royalties) while at the same time allowing people to download music from the Web easily.
Stay tuned for further developments!!