Runners expect a degree of soreness in the legs after a workout. In fact, they often enjoy the soreness as a "badge of honor" signifying a difficult but successful workout. However, it's also possible to experience soreness in the neck after running. It's not usually an emergency, but rather a sign of poor running form.
Running bounces your body up and down through the course of a workout. If your body is properly aligned, the natural structure of your skeleton supports this bouncing and you'll experience few problems. If your head is hanging too far forward, the bouncing of your relatively heavy head will put strain on your neck. That muscle strain can result in soreness.
For minor cases of neck pain from exercise, including from the jostling of a running workout, apply ice as soon as possible after the session to help alleviate the pain. Ibuprofin or similar anti-inflammatory pain medications will also help, especially in cases of "second-day soreness" that often restrict motion.
Proper alignment is your best defense against a sore neck from running. This means running with your spine relaxed but straight. Your head should be above your shoulders and your shoulders directly above your hips. While running, pay attention to your head and lower back. Tucking your head forward or leaning forward at the lower back are two common ways to disrupt this alignment and cause neck soreness.
Also, feel if you tend to tense up and squeeze your shoulders up by your ears as you run. This can also bring on neck soreness.
Common Sense Caution
A sore neck from muscle strain is a painful but minor injury. However, neck pain can be a sign of more serious conditions.
If the pain is sharp, consistent or accompanied by numbness or shooting pains to other parts of your body, check with your doctor as soon as possible. Running may not be the cause, but aggravates pain from a pinched nerve or herniated cervical disc. Don't go back to running until you've gotten the "go ahead" from a medical professional.