Update: Apple has updated its status page to reflect outages for multiple services including the App Store, Mac App Store, iBook Store, and a few iCloud services:
Many users (and Apple’s own iCloud Status Page) are reporting the inability to make purchases from the iTunes Store on both iOS and the OS X iTunes Store. Some users are also noting difficulty with downloading apps from the App Store, but Apple does not say that the App Store is officially seeing issues. However, the App Store and iTunes Store are seemingly all part of the same system, so perhaps issues from the iTunes Store could affect app downloading as well.
Update 2: Apple now says everything is back online:
Update 3: Now FaceTime is down for some.