There are three very effective ways to strengthen and enlarge your neck and I recommend that you do at least two of them since they target different parts of this body part. The first and the most effective one is to train your neck with a neck developer, like this:
I’ve seen plenty of boxers train like this, and if you follow boxing you should know that most of the competitors have strong muscular necks compared to the average individual. You can easily buy a neck developer from a sports store or from E-bay… then all you have to do is attach some heavy thing to it, like a disc plate, assume a standing or flat position as shown above, and start lifting your head up and down until your neck tires out. With this exercise you should be able to enlarge and strengthen your neck significantly in a very short amount of time.
The second method to strengthen (a different part of) your neck, is to perform shrugs. This method doesn’t enlarge the neck itself (the front part), but it will build up your upper trapezius muscle (known in bodybuilding circles as traps), which consist of the base and back of the neck. The famous boxer David Tua is a great example of a man with large traps: