Affected customers are getting a popup message that reads: "The iTunes Store is unable to process purchases at this time. Please try again later."
The App Store issues have been ongoing for approximately a half hour now, but no outage is listed on Apple's System Status page.
We'll update this post when the issue is resolved. Problems like this are often fixed quickly, so apps shouldn't be unavailable for too long.
Update: Apple's System Status page now displays issues with the App Store, Apple TV, iTunes U, iTunes Store, Volume Purchase Program, and Mac App Store.