Over 5 Billion apps have been downloaded from the Apple App store - 1.5 billion in 3 months

"The two biggest stats Jobs said for last. There have been over 5 billion app downloads so far. And Apple has paid out over $1 billion to app developers (their 70% cut of all sales)."
Source: Taken from Steve Jobs' keynote to the WWDC event in San Francisco, reported by Techcrunch, 7th June 2010
Previously - 4.5 billion downloaded (9th April 2010) 3 billion downloaded (5th Jan 2010) 2 billion downloaded (28th September), 1 billion downloaded (24th April 2009)