Are Nightmares Normal?
Nightmares ARE normal.
Who Has Nightmares?
Both children and adults can experience nightmares but they are far more prevalent in children with an estimated 20-39% of children experiencing them versus 5-8% of adults.  Nightmares typically begin between the ages of 3-6 , peak between the ages of 7-9, and begin to decline in frequency by age 10. In young children, both boys and girls experience nightmares equally, but between the ages of 13-16, girls experience a higher frequency than boys do. 
Why Do Children Have Nightmares?
Nightmares in children are normal and very rarely signify an underlying illness.  They usually begin around age three because this is the time that normal fears develop and imaginations are highly active. Nightmares can be a child's reaction to trauma or stress, an insecurity at a particular stage of development, or any situation that the child feels is unsettling. They begin to decline as the child matures, has a better understanding of the world, and has less separation anxiety. 
Why Do Adults Have Nightmares?
For the occasional nightmare in adults, there is usually an outside force that triggers a nightmare. Like children, adults can have nightmares due to trauma or stress. Alcohol and medications can also trigger a nightmare. They can also be triggered by eating heavily before bedtime, which increases metabolism and brain activity.  For a list of foods that trigger nightmares see Does Eating before Bed Cause Nightmares?
When Are Nightmares Not Normal?
The occasional nightmare is normal even for an adult. When terrifying dreams are recurrent with recollection and involve threats to self-esteem, safety, or survival they are considered a nightmare disorder.  Many things can contribute to frequent nightmares that are outside of the normal occasional nightmare and can include:
Side Effect of Medication. Several medications can cause recurrent nightmares that include drugs that alter neurotransmitter levels that are associated with nightmares are alpha agonists, beta blockers, levodopa, monoamine oxidase inhibitors, rauwolfia alkaloids, selegiline, and tricyclic. Drugs with withdrawal effects that are associated with nightmares are barbiturates, benzodiazepines, and ethanol. Additional drugs associated with nightmares are flutamide, ketamine, procarbazine, and short-acting barbiturates. 
Melatonin, which is a supplement that some take to assist in sleep, has a side effect of vivid dreams and nightmares for some. 
Underlying Health Condition. Several health conditions are associated with nightmares including angina, REM sleep-associated apnea, abdominal pain, headache 
Sleep disorders . Several sleep disorders are associated with nightmares including sleep apnea, severe anxiety and depression, narcolepsy, restless leg syndrome, and night terror disorder. 
Underlying Psychological Condition. Several psychological conditions can trigger nightmares such as anxiety, depression and post-traumatic stress disorder