Reports from iMore readers, as well as other outlets, have confirmed the issues. Basically, users can log into the app stores but cannot download any applications. In addition, other reports from outlets like The Next Web state that services like Tunes Connect and TestFlight are not working. This situation has been going on for the past few hours.
Update: Apple's online service status page now shows that the outage has been going on since a little before 5 a.m. EDT. The outage affected not only the iTunes Store, but iCloud account and sign in, as well as iCloud Mail. However, the iCloud-related outages appear to have been resolved. Apple notes that the iTunes Store outage is impacting all users.
We will update this post when these services are back up and running.
Source: The Next Web; Thanks to everyone who tipped us!