These are the fix's available to original Mac users, should work for Hackintosh too.
Hackintosh Solution (Applicable for Hackintosh Only !) :
Download patched chameleon and FileNVRAM.dylib from iMessage_Fix folder in downloads.
Install the patched chameleon and drop the FileNVRAM.dylib to the /Extra/Modules folder (create Modules folder inside Extra if you had not created earlier).
If the Modules folder had ACPICodec.dylib already, delete it.
Reboot, sign in to iMessage. If this solution does not work, proceed with the fix's below.
(The solutions below are applicable for both hackintosh & Mac) :
Solution 1 :
Check that your hosts file (/etc/host) is not blocking some important communication with Messages or game center.
Open hosts file in TextMate and commented out everything that was not default, saved it, restarted Messages and GameCenter, then logged in.
After logging in , uncomment the comments in my hosts file, save it, and check everything.
Solution 2 :
Quit imagent process from Activity Monitor and try logging into iMessage again.
a. Go to Keychain Access
b. There will be a certificate issued by Apple iPhone Device CA – This certificate was signed by an unknown authority. Delete this certificate (or move it to the desktop, out of the keychain access store)
There are some references where you need to set/add your DNS to 220.127.116.11.
Then check logging into iMessages again.
Solution 4 :
Just click on the “Time” in the top bar of the computer and choose “Open Date & Time Preferences”.
Then enable “Set date and time automatically” and check the iMessages again.
The official Apple resolution for the above issue is found here - http://support.apple.com/kb/TS3970?viewlocale=en_US&locale=en_US