We've been getting reports from some people, in some parts of the world, unable to get to the iTunes Store or to download apps. As of now, Apple System Status is reporting problems with the iTunes Store, but not yet the App Store. Since they're connected, it's safe to assume the problem is pretty general.
If you're having trouble accessing iTunes Store or downloading apps, let us know where you are, when your trouble started, and when it starts working again!
Update: Apple is now reporting App Store, Mac App Store, iTunes Store, iBookstore, iTunes in the Cloud, iTunes Match, and Backup are all down, down, down.
Users may be unable to make purchases from the App Store, iTunes Store, Mac App Store, or iBookstore. Users may also be unable to download previously-purchased content, use iTunes Match, or successfully restore Apps and Music from an iCloud backup.
Not much to do but wait and hope Apple gets their WebObjects all swept back in order quickly...
Update 2: Apple is reporting all services restored as of 10:54am PDT. Everything working for everyone again?