You already have a ton of options when it comes to cloud-based music, including iTunes Radio, Pandora, Spotify, Rdio, Amazon Cloud Player, and more. Yet you might want to consider Google Play Music, since it offers a combination of features not otherwise available. As you know, services like Pandora and iTunes Radio let you listen to songs similar to what you like, but you're unable to request specific songs. And subscription services such as Spotify and Rdio let you request a particular song and typically charge a monthly fee of around $10, but they don't store your personal collection in the cloud. Then there are services like iTunes Match and Amazon Cloud Player that let you upload your collection to the cloud and stream music that you already own. Google Play Music combines the ability to request specific songs (like Spotify and Rdio) with the ability to upload your music collection (like iTunes Match and Amazon Cloud Player).
A very helpful article on TidBITS explains why this might appeal to you. The article notes that neither Spotify or Rdio has music by, for example, the Beatles or Led Zeppelin. But you might very well have that music in your own collection. The advantage of Google Play Music, therefore, is that you have all your music available to you in the cloud, plus you have available to you for streaming or downloading a universe of music you don't already own.
Google released their free Google Play Music app for the iPhone in mid-November. The TidBITS article explains that Google's service that lets you upload music is free up to 20,000 songs. If you also want to be able to stream songs you don't already own, then you'll need to opt for their All Access tier, which is $9.99 per month and gives you unlimited streaming from Google's catalog of 20 million songs.
The TidBITS article also walks you through the several components of Google Play Music. These include Music Manager, the desktop app that you use to upload your music, Google Play Music on the Web, which lets you manage your collection of music in Google's cloud, and Google Play Music on iPhone, which lets you manage your collection and stream music to your iPhone. As I understand it, the All Access tier actually lets you download and store music on your phone for offline listening.
Overall, the review really likes this service and says that one big advantage is that you can access your account via multiple devices.