In Japan, the government recognizes the Dai Nippon Butokukai and the Kokusai Budoin as governing bodies while in Korea, they oversee the Kukkiwon (Taekwondo only). While I am adamantly against a single governing body that oversee's all martial arts on behalf of state or national governments, I believe every instructor should be certified by some organization with a reputation for quality control.
If you are an independent practitioner, or are an instructor/founder of a modern art with no governing body, it is a good idea to look for a multi-style organization that best fits your needs. While this article is not meant to be an advertisement for our group, the US Association of Martial Arts along with our affiliate organizations (the Ryu-Sakura-Do Karate Federation and World Organization of Mixed Martial Arts) is known throughout the martial arts community for adhering to the highest standards of quality control and legitimacy. Whether you join our organization or another one is irrelevant. There are certain things which you should look for, and I cover in-depth in the previous article, "Prestigious How?"
While not required, belonging to an organization lends credibility to your instruction and lets the public know that the instructors they are entrusting their lives and their children's lives to have been thoroughly trained and certified. In today's society, we don't even let a cosmetologist or barber cut our hair without being properly licensed. Shouldn't it be common sense to demand the same from those whom we learn the skills necessary to defend ourselves and our families?
As instructors, it is up to us to raise the bar of martial arts instruction here in the States and across the globe. With the abundance of charlatans posting nonsensical videos all over social media, and subsequently being torn apart by martial arts of all backgrounds, we need to step up and show the public that legitimate, traditional, effective martial arts still exist. This can only be done if we work together, something your governing body should be actively striving for. If the organization you belong to only exists to collect fees and issue paper, what purpose do they really serve?