updated 05:20 pm EDT, Tue April 9, 2013
AT&T, Verizon users affected, no estimated time of repair
[Updated with recovery information] Apple is reporting that "some users" are affected by an outage affecting both iMessage and FaceTime communications. Users on the Apple Support forums are claiming that both services and display a "waiting for verification" message in lieu of sending the message or syncing a FaceTime call between participants.
The problems seem to be more prevalent on the iPhone 5. Some users are reporting that outgoing messages will ultimately be sent by SMS after trying iMessage, but this is not universal. Both AT&T and Verizon users are affected by the issue, suggesting a problem with Apple or critical networking equipment associated with the manufacturer.
Apple's service page shows that the outage has been going on since about 3:15 ET. The company has made no statement on what the problem is, or when full recovery is expected.
Update: After acknowledging the incident tersely, Apple noted that full service was restored at around 8PM Eastern Standard Time to all users.