Magnatune: We Are Not Evil. Listen to "over 500 hand-picked complete albums" for free, buy DRM-free downloads for "as little as $5," or buy a pressed CD. Their catalog is licensed for free use in non-commercial projects, so they're a good source for background music and intros of non-commercial projects, and commercial licensing is also available. Also look for Magnatune podcasts in the iTunes podcast directory for tons of ad-free no-cost music. Their classical selection is limited, but of high quality.

Their free listening venues all include a short tag at the end of each track, stating the title of the track, album and name of the artist. ("That was track number 5, from the album XYZ by ABC, from Magnatune.com.") The length and placement of the tag is seems reasonable for most kinds of music, but it's annoying for classical, which doesn't really need each movement of a piece to be announced.