This is a great article by Peter Bright at Ars Technica that explains why any company would be foolish to fork Android. More significantly, it highlights the difference between Android Open Source Platform (AOSP), which is open source, and Google Mobile Services (GMS), which is not.
The split between AOSP and GMS is not constant, either. Google has slowly been migrating more and more functionality to GMS. For example, in the latest Nexus 5, the core phone user interface—the thing that you use to launch apps and show icons—has been rolled into the GMS Search app.
Similarly, APIs have made the move. AOSP contains a location API, but GMS contains a newer, better one, with additional features. Google encourages developers to use the GMS API, and the AOSP Location API mostly dates back to Android 1.0, and hasn’t seen any substantial changes since Android 1.5. The result is that many third-party applications are not merely “Android” applications: they’re GMS applications, and won’t run without the proprietary, non-open Google software.
It’s possible to only use AOSP and try to fill in the missing GMS apps on your own, but you’d never keep pace with the GMS development and you wouldn’t be able to use any third-party applications that use any GMS API features.