It started with a few tweets and progressed to our own internal tests, and it would appear as though Apple's iTunes servers are, at some level, not working properly. For me, it began with an all-too-familiar timeout while trying to update apps. Then I tried to download the currently-free Plastic Bullet app. Later, when we started testing, it appeared that the issue had turned into a sign-in issue with authentication servers refusing the connection.
Steve and Chris in Colorado, meanwhile, are seeing slow downloads but are able to log in and download apps. The issue appears in iTunes and Mac App Store. Let us know if you're seeing this in the comments.
Update 2: This appears to be affecting iTunes Connect.
Update 3: As of 9:20 ET, it appears things are starting to stabilize with Apple's servers. Both I and Megan up in Pennsylvania were able to authenticate, however Megan is getting errors stating she already purchased an app when she hadn't bought it yet.