Pandora lets you create music stations based on a genre, band, or song you like, and over 400 music characteristics are taken into account when it chooses your next song. Pandora's a great way to discover new music that's rooted in a style you already enjoy, and if you hear a song you like, you can buy it right from within the app. You can listen for free if you're willing to put up with ads, or you can pay $4.99/month for Pandora One, which is ad-free and streams music at a higher quality bitrate.
Price: Free to download ($4.99 for Pandora One, a premium subscription)
Available on: iOS, Android, and Windows Phone