I've come up with GSMTAP about two years ago while working on airprobe. The goal was to have something similar to what radiotap does in the wifi world: A pseudo-header that adds additional information and context that is not present in the actual message.
Initially, GSMTAP was intended to be a separate link-layer type in the pcap file format, but this would preclude its use in real-time protocol analysis. So I modified it to be encapsulated in UDP packets, which are sent and received using normal UDP/IP sockets.
Over recent years, GSMTAP has not only been integrated into multiple programs of the airprobe project, but is also understood by wireshark. OpenBTS has also decided to adopt the format and can generate GSMTAP messages for debugging purposes.
After creating OsmocomBB, it was taught how to generate GSMTAP messages very quickly, too.
So by now, at least when it comes to Free Software, it is definitely the de-facto standard for capturing/transmitting and analyzing protocol messages from the GSM air interface.
However, until now, there has never been any official "homepage" of the GSMTAP header. This has changed now, the GSMTAP homepage is now part of the OsmocomBB wiki.