Unfortunately, there is not currently a way to mandate and keep tabs on every single running race in existence. This is because small towns, student organizations at colleges and universities, non-profits and even just volunteers trying to raise money for a cause can technically put on a small race whenever or wherever they want, so long as they have support from the city and public servants like police officers to block off streets and emergency medical help just in case something goes awry. So, for this reason, there is no real way to know of every single running road race that is set to take place all over the world.
However, there IS a governmental body or organization that is in charge of governing road races - particularly larger races that attract a bit of a crowd. This organization is the IAAF: the International Association of Athletics Federation. The IAAF, founded in 1912 in Stockholm, Sweden, functions to keep tabs on what races are being held, when they are being held, who is running them, and where they are located. They are the world governing body for all track and field athletics. That's right - not only is the IAAF responsible for making the rules and regulations for road racing, but for track and field events as well.
For distance races, the IAAF sets the rules for which distances are "IAAF recognized." These include the 5k race, the 10k, the 10 mile, the 8k, 15k, 20k, half-marathon, 25k, 30k, and the 100k. The IAAF also host the IAAF World Championships every other year, with a rotating location. Athletes representing counties from all over come to compete in 10 days of various distance running events, track running events, and field events. The 2017 IAAF World Championships were held in Great Britain, while the 2019 World Championships are set to be held in Doha, Qatar.
And while there is no way to track every single racing event that is held, to give you some idea, there are certainly thousands of road races at varying distances held all over the world each year.