I'd been hoping for a while to see this data released from the BBC: given a particular artist, find out which radio shows played that artist most often. Luckily, a set of data for the last 6 months was released for Mashed last weekend (though it's a bit incomplete as not all tracks are recorded for the late night 'experimental' shows, apparently).
Patrick Sinclair made a web app to recommend shows using latent semantic indexing, but not an API that can be queried directly, so I've imported the data into a database that can be queried by artist (and as JSON too).
You can download the SQLite database and PHP scripts directly, if you prefer to work with the data elsewhere.