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I've seen a couple of different topics about this but none that really detail my problem. I transferred from MobileMe to iCloud when the transition first started (I use a @me.com email address still) and iMessage has always worked fine. It seems the last couple of weeks (maybe since MobileMe officially deactivated?) I can't send or recieve iMessages (both on my phone, iPad and now on Mountain Lion) using my Apple ID as the caller ID. If I set it to my number everything works fine, but the moment I set it to my me.com email address everything just sets to "Not Delivered" with the red exclamation mark. What's strange is that SOMETIMES the messages go through, even when it says not delivered. Everyone texting ME also gets Not Delivered, even if I may get the message.
I've tried resetting network settings, I've tried restoring a back up and I've tried completely restoring my phone in a clean restore, nothing seems to work. And now (I know this isn't the right section) but Messages for Mountain Lion is doing the Not Delivered thing too. I'm assuming it's just a problem with my Apple ID?
By the way, I have an iPhone 4, an iPad 3 and a MacBook Pro and it happens on all of them.
Here is how I fixed mine. I have 2 MacBooks and and iPhone. On the Messages app on the MacBooks I went to Preferences>accounts and disabled them. I then quit the application. Next I went to ~/library/messages and deleted everything in there. I then re-opened the messages app and re-enabled my iMessage account. All is well now.
^ I had a similar solution.
It seems the issue was the beta version of Messages I had on my iMac. The beta had stopped working a long time ago on my iMac so I just ignored it and left it, waiting for Mountain Lion. As soon as I installed Mountain Lion and cleared the beta Messages, iMessage started working on every one of my products properly.

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