Pandora is one of the original Internet radio apps. The "stations" are actually custom music streams tailored to your choice of artist and genre. Pandora lets you listen to specific songs or artists, create playlists and find new tunes. Pandora's software draws on and analyzes a huge database of tunes to keep presenting you with new music based on your favorites and your listening patterns. The app also lets you e-mail your stations to your friends, bookmark particular songs and buy tracks directly from iTunes.
Using Pandora's mobile app, you can see album art, read about artists and check the songs you've just played. There's a free version, but a paid subscription gives better streaming quality, no advertisements and unlimited listening.