Apple has now made available its 2013 12 Days of Gifts app for free download in the App Store. In the past Apple has offered this app in other countries, but for the first time this year it's also available for download in the US. From December 26 to January 6, you'll be able to download a free gift each day: songs, apps, books, movies, and more. Each gift will only be available for 24 hours, so you'll want to check the app every day to see what's available.
By the way, according to a post on AppleInsider, Apple is also offering eight free Christmas songs as part of their "Holiday Cheer" promotion. You download the songs via the free Apple Store app. The offer expires December 31.