Apple is finally debuting its popular iTunes media store/application across most of Asia and other regions, it announced today.

The iTunes store will now be available to customers in Russia, India, Turkey, South Africa, and 52 other countries. Those customers will gain access to the bulk of music from major record labels as well as offer a selection of local music artists from their own countries’ or regions. Apple states that there will be over 20 million songs available for purchase in these new international iTunes stores.

That means these countries will also finally have access to Apple’s iTunes Match service, which allows you to back up your entire library within the cloud, and download or stream your music from any Apple device. And of course, users in these countries will also gain access to the iTunes App Store.

Movies are a different story, as only certain countries will be able to purchase films from the major studios, including Russia, Turkey, India, Indonesia and others.

Apple just rolled out a new version of iTunes (version 11), which offers significant upgrades to the media player, store, and overall user interface. And apparently the new version was good enough to expand into these other countries.