I've already mentioned the wondrous Spotify.
Problem is that you need to be in the right country, you need to have an invitation to use it for free, and most troublesome - you need to install client software - which is not always possible. At work for example.
But Grooveshark has a similarly enormous collection of music to amble through - and runs using a browser with Flash only. Easy.
I have a penchant for popular classical music and was searching for versions of Air on the G String (stop giggling, it's just a pretty piece of music).
Anyhow - Grooveshark offers you the usual suspects - UK Symph, Academy of St Martin in the Fields, Nigel Kennedy, Yo-Yo Ma etc - but also a version by "The Fucking Champs". Sadly it was a dull piece - but a glorious example of gratuitously offensive and wilfully stupid band naming.
Anyhow - Grooveshark.