More than 4 billion apps have been downloaded from the Apple App store

"Today, more than four billion apps have been downloaded from the revolutionary App Store and more than 185,000 apps are available to consumers in 90 countries. Over 85 million iPhone and iPod touch users around the world can choose from an incredible range of apps in 20 categories, including games, business, news, sports, health, reference and travel. "
Source: Apple press release, 8th April 2010
Previously - 3 billion downloaded (5th Jan 2010) 2 billion downloaded (28th September), 1 billion downloaded (24th April 2009)
UPDATE - Apple now say that 4.5 billion have been downloaded