I still have hope for this question and would like to get some good resources so I'll give it a start at least. I can discuss some of the resources I use from nuclear/atomic physics but I would love to hear about some organizations in other fields. I know that many of the people on this site are either students or theoreticians, but in the "real world", it is important to have cooperative recognition of acceptable practices, principles, and data.
I am a (junior) measurement specialist for a nuclear facility; it is essential to understand official systems of measurements and legal metrology. Acccordingly I rely on:
- Bureau International des Poids et Mesures (BIPM)
This is the organization that defines and maintains (at the behest of the JCGM) the international system of units (SI). They periodically publish a brochure with the official definitions (in French) and an unofficial English translation. They also set the standard for citation of measurement uncertainty.
- National Institute of Standards and Technology (NIST)
This is the US equivalent of the BIPM. They maintain national standards that are used for calibration purposes and provide calibration services. Additionally, their website provides links to several other organizations and to some good free software.
- The American Association of Laboratory Accreditation (A2LA)
This is the primary certifying body for analytic and calibration laboratories. For working facilities, it is pretty much essential to acquire and maintain certification.
- International Organization for Standardization (ISO)
This is an international body that sets standards for everything from toilet systems on boats to proper calibration laboratory technique. Federal law in the US pretty much mandates compliance with ISO standards in many fields and A2LA requires compliance with ISO 17025 for laboratory certification.
- Committee on Data for Science and Technology (CODATA)
As I mentioned in the question, CODATA provides the latest publication of fundamental constants. Most software keeps up to date with CODATA, but it is important to know the source of your information and their publications can make for some interesting reading.
- ENDF / JENDL / CENDL / JEFF / ROSFOND cross section libraries
These are the official repositories for cross section data for the US, Japan, China, Europe, and Russia respectively. You can get access to the raw data from places like the national nuclear data center but typically these libraries are used by analysis programs. Again, it's good to know your resources nonetheless.
- Radiation Safety Information Compuational Center (RSICC)
Many of the programs that make use of the cross section libraries are available through RSICC. It is not uncommon for them to require a security clearance or a sponser to get access to the software, but they have some very useful stuff.
- Idaho National Laboratory (INL)
I'm not sure how official it is, but INL has catalogues of the gamma spectra of a huge variety of isotopes.