First spotted by Macstories, the official countdown ticker is viewable within iTunes under the App Store section.
From the countdown page:
Apps have revolutionized the way we play video games, consume news, do business, education, communicate, create art, and so much more.
The performance of the App Store has been overwhelming, steadily growing in size and revenues since its launch in 2008. As an example of the store's explosive growth, Apple launched a similar countdown to 1 billion app downloads in April 2009, which was followed by a promotion for the 10 billionth app download in January 2011. Most recently, Apple started a countdown ticker to 25 billion downloads in February 2012, meaning download rates roughly doubled over the past year.
In addition to the $10,000 gift card for the 50 billionth app download, Apple will also award a $500 App Store Gift Card to the next 50 customers following the momentous download.
The iTunes page also has an updated list of the top all-time paid and free apps, with respective number ones being Angry Birds and Facebook.
As with any sweepstakes and giveaway in the U.S., no purchase is necessary, and Apple has setup an alternate entry webpage for those who don't wish to buy an app or download a free title. At the time of this writing, the page was still under construction.