We have seen several reports of that the iMessage service provided by Apple is having some problems and messages in many cases are failing to deliver between i-devices.
This also seems to affect other APN (Apple Push Notification) services such as those provided in many apps available on the iTunes App Store.
The current prevailing theory is that message traffic generated in the wake of Hurricane Sandy may have caused Apple to need to add capacity to their APN systems, which has left many "tokens" unable to be used (a "token" is a unique identifier stored in your phone to help it let Apple's servers know who you are and what services you should be receiving).
Another theory is that Apple's North Carolina data centre is being slammed and has had to drop some services. Those services are being re-routed to other data centres.
Right now, the best fix seems to be to simply restart your iPhone or iPad (if it is having trouble successfully sending a message).
If you are in the affected areas, you may also experience data outages (e.g. your own ADSL and WiFi), in which case iMessages and other notification services may not work anyway. In such cases, disconnect your iPhone/iPad from the WiFi network (if ADSL/cable internet is down) and try using your carrier's 3G network instead.
Our best wishes go out to our friends and customers on the East Coast of the U.S..
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