There are probably many more laws on the books than what is described below but this list gives you some information on a few common ones in our industry.
Building codes in the US have adopted the IBC/ICC codes for rules related to various building types. For Steel Buildings, The IBC refers to AISC 360 which in turn refers to AWS D1.1. The link below will open up the IBC that existed at the time of this writing.
Each individual states Department of Transportation has rules and those rules may have specific requirements for testing such as who witnesses it, what tests are required etc.. But for the most part, the requirements will refer to an existing code or standard such as AWS D1.5 and AWS D1.1. The link below will open up the Virginia Department of Transportations requirements.
Transmission pipelines are regulated by the Federal Government.
49 CFR Subpart E 192.227 refers to existing codes such as API-1104 and ASME IX but for Low Stress Pipe, special rules are allowed. See https://www.law.cornell.edu/cfr/text/49/appendix-C_to_part_192
Boiler and Pressure Vessels
In the US, each individual State has laws related to the installation and repair of boilers and pressure vessels. In most cases, the requirements for the qualification of welders will be governed by ASME Sec. IX which is referred to in the actual codes of construction and the National Board Inspection Code (Used for Repairs and Alterations). The link below will take you to the Law in the State of Tennessee.
I am sure there are many more cases in which a law exists about a welded product. For the most part, they will refer to existing codes and standards. If you are performing welder qualification testing be very careful about what you "sign for". The welder performance qualification record should clearly state what you are "certifying"
There are many agencies, industry groups, and jurisdiction out there that may have very stringent requirements. I am writing this lesson from the experience of a person who has NOT experienced everything in the welding industry. INdividual states, counties or cities may have some specific requirements. If you are performing testing for another entity, make sure they know they are responsible for following all requirements.
Feel free to contact me if you think something could be added. If you are aware of any welding related litigation related to "certified welders" please let me know. I have been searching. I have found cases where they were no but none where they were and the certifying organization was held liable.