If you can take a punch or kick and not go down, you have a fighting chance (no pun intended) of winning. Because you have built a string neck, shrugging off a good shot, will invariably make your opponent question their ability and yours to some extent.
Having a strong and mobile neck can reduce the chances of whiplash type injuries because your neck will create a wider base for the head to sit upon, but also slow down the head once impacted, this leads to less brain shake. In some contact sports such as MMA & BJJ, a thicker and strong neck can also offer protection to the carotid arteries and other major blood vessels that supply the brain. A thicker and stronger neck can better withstand compressive effects of a choke or other forces applied to the neck. Like all muscles, if you can generate greater levels of tension and rigidity, the amount you can withstand goes up.
With combat sports, there are so many disciplines which a fighter has in his/her armoury, these include throws, grappling, stand-up and traditional martial arts, you neck, head and upper body will take a pounding, combining neck training with your strength & conditioning will help you become a better all-round athlete.
In short, a strong, mobile and conditioned neck, will help you last longer in a fight, reduce your chances of concussion type injuries, which will increase your overall longevity in your chosen sport.