We all believe that warm milk promotes sleepiness because of the tryptophan contained in the milk. Tryptophan, the sleep-inducing amino acid, is found in our Thanksgiving turkey and in milk, and thought to have a sedative effect. However, if you're going to rely on a glass of warm milk to act as a sleep-aid, it is best to pair it with some type of carb, e.g., crackers, bread, etc. The high-carb snack will cause your insulin level to go up, which in turn, will act as a catalyst for the tryptophan to cross the "blood-brain barrier."
If you swear by warm milk as a sleep aid, studies reveal that warm milk does have a calming influence. The milk, without the carbs, however, is more likely just a placebo effect.
Silber BY and Schmitt JA. Effects of tryptophan loading on human cognition, mood, and sleep. Neurosci Biobehav Rev 2010;34(3):387-407.
Wurtman RJ et al.Effects of normal meals rich in carbohydrates or proteins on plasma tryptophan and tyrosine ratios. Am J Clin Nutr 2003;77(1):128-32.