MPme on iPad says it's a 'curated radio' app but who really knows what that means? It's basically a pretty-looking collection of streaming stations, but the app also recommends shows, artists and tracks based on what they, and you, are playing.
You can search through tracks you've played to find your favourite artists, tracks and stations and buy music on iTunes if you want it all the time. It's Wi-Fi and AirPlay compatible, will hook up to Facebook and Twitter for social recommendations, and iPhone and Android versions are on the way soon.
A brilliant, free curated radio app which means you'll never have to think about what to listen to next again