Why the issue occurs
One very common issue with Hackintoshes is an inability to log in to iMessage, iCloud, ect. There have been various fixes for the issue; however, they are somewhat scattered throughout forum sites; I will attempt to assemble them here.
There are two basic reasons:
Apple computers store a lot of their identification information in their BIOS. This causes a lot of issues for hackintoshes because OS X assumes that information will be there, and it cannot boot without it. We get around this issue by injecting SMBIOS through our bootloaders. This way OS X believes it’s running on a real mac and can access all the identification stuff it needs to run. However, Apple’s services attempt to read the serial number of the motherboard, which they cannot do on a hackintosh. This causes them to fail.
The second issue is a result of OS X’s naming convention for network interfaces. Hackintoshes use a much wider verity of wireless cards, so they may end up with an identifier that OS X and Apple’s services may not be designed to handle.