Provided Apple and/or AT&T don’t throw a fit, you’ll soon be able to use Rhapsody on your iPhone (and iPod touch). The App works over 3G and EDGE (and Wi-Fi, of course), streaming music from a library of more than 8 million songs.

The App is being submitted this week for Apple to review; hopefully it’s not rejected for some lame reason. It seems to work easily enough: launch the App, search for your song, and away you go. You can, of course, also browse by artist, album, etc. Pretty simple and about what you’d expect, not that there’s anything wrong with that.

If you’re not familiar with Rhapsody music-on-demand service, just think Spotify—execpt that it works here in the U.S. with having to find a UK proxy server or using a beta. (I, for the record, have access to the Spotify beta. Perks of the job, I suppose.) Rather than download an MP3 or AAC (or whatever other kooky format you can think of), you merely stream the song on-demand. The video shows U2’s “Beautiful Day” playing as soon you hit play.

The benefit to streaming is that you have instant (if your Internet connection plays nicely) access to a boatload of songs, versus how ever many you have on your iPod. Of course, Rhapsody (or Spotify or NameYourStreamingService) could go bankrupt or otherwise blow up, suddenly leaving you without access to Lady Gaga. That’s not a world I want to live in.

But yeah, Real has submitted the App. If/when it comes out, I’m sure we’ll have a look-see. Oh, and Real is working on an Android App, but it’s not done yet. Sorry.