According to a number of readers and our own observations, it seems iCloud is in the midst of a somewhat widespread service outage that has been going on since roughly 4PM Eastern Time. Users are unable to access mail and other services either via standalone applications on the Mac or iOS, or via the iCloud website.
Apple's iCloud service status website doesn't indicate any issues, which may suggest the outage is not serious enough to warrant a notice or more likely that Apple simply hasn't updated the page yet.
Update: Apple has now added a notice to the system status page acknowledging the outage.
Update 2: Service seems to be restored.