Free MP3 Downloads from Amazon.co.uk
Offers regularly changing free album samplers and singles, usually from new/upcoming artists, but often there are knows artists in the list too.
Free Music Downloads from Last.fm
A large variety of free singles to download.
Powered by Last.fm, allows bands to give away MP3s as a way of promoting themselves and getting their music heard.
Free downloads from independent or underground artists (mainly from the US).
Insound Free MP3s
A CD/Vinyl online shop that gives away free indie MP3s, mostly from US Groups, some well known ones. The files seem to download without an extension, so won't play initially, but adding '.mp3' to the end of the filename fixes the problem.
Matador Records MP3 Archive
No longer updated, but as lot of old (pre 2007) songs still on there.
Over 350,000 tracks to download or stream free, mostly from independent artists.