I *think* I have it solved. I've had loads of problems with iMessages and I've contributed to 3 threads on the subject. I'm going to post this 'solution' to all 3. Forgive the size of this post, but I think the story is important to help others.
First the back-story:
iMessages was hopeless. Messages not sending unless I 'woke' it up. Messages not syncing and messages addressed to my phone number only sometimes showing up on my Mac even though I had iOS6.
As a note, I was an iMessages beta user. Also, you will need iOS6 on your phone (I think).
Now, this is what I did and everything is now working. Don't worry about the fact I did a fresh Mountain Lion install as I think that is a step you dont need. However, here is the full story as some of it may help. I'll try and extract the things you need to do at the end.
During a fresh install of Mountain Lion on my Mac Pro (I have that and a MBA) the Mac asked for my AppleID. I gave it. About 15 mins into the install (with another 15 to go) my iPhone beeped with a pop-up message "Mac Pro is now using xxxxx for Messages" where xxxxx was a list of my mail addresses AND my mobile number. It was like the Mac and the iPhone had a conversation and decided it was OK. So I looked to see if I could add my number to messages on the MBA. There's no option to do this (that I could see). To check what Messages is using on a Mac, open Messages, go to Preferences, then Accounts, click on the iMessages one and you get a list. My mobile number wasnt there.
So, I signed out of that account and tried to sign back in again. It didn't work (sign in failed with no error message). I tried 2 more times. On the 3rd try a 2nd iMessages account was created (the first said it was inactive). A few seconds later a message poped up on my iPhone telling me that the MBA was now using the same list of email addresses for iMessages my Mac Pro was AND crucially, my phone number. At this point I deleted the inactive iMessages account.
I then had to restart Messages
Now everything syncs perfectly.
So, my tip. Make sure you have iOS 6. Delete your iMessages account in Messages on your Mac and then add it back (effectively signing in again). This forces OS and iOS to re-sync and I think that everything is fine after that.
Rob.