Pandora allows you to listen legally to customized radio for free online, but unfortunately it is likely to soon go out of business. If you haven’t tried it, you should (although I believe it’s only available here in the USA). They even have the Beatles!
The great thing about it is that Pandora has such a large selection of music, including classical music. All you have to do is put in the name of a composer and Pandora will play music by that composers and others from the same era. For instance, I never get tired of listening to this Vivaldi station.
I’ve also discovered lots of interesting music through this Scott Joplin station.
I hope the links work!