30 billion apps have been downloaded from the iTunes app store

"Apple CEO Tim Cook [has] announced that the company is now host to over 400 million accounts on the App Store, with more than 650,000 apps available to customers.
Cook added that 225,000 of them designed for iPad and 30 billion apps have been downloaded in total.
Putting things into perspective, Cook said that the App Store is now operational in more than 120 countries, with 35 more to be added by the end of this month.
[...]
Focusing on developers (it’s a developer event after all), some $5 billion has been paid to developers since the launch of the App Store."
Source:  Tim Cook, speaking at WWDC, Reported by TheNextWeb, 12th June 2012
Earlier - 25bn announced on 5th March
10bn announced on 22nd January 2011

5bn announced on 7th June 2010

1bn announced on 24th April 2009