Actually, there is some research on melatonin in sleep medicine. We know that this hormone is important for sleep regulation (cyle of sleep). Some studies suggest a positive effect on jet-lag. One study showed that 30 % of patients taking Melatonin, 2 mg, in a slow release form, got improved sleep, compared to 20 % for a placebo medicine. But I do not think it is worth to buy this supplement for such an indication.
Some patients use it for chronic insomnia. Advertisements promise no negative effects of melatonin and no dependence. However the effects on insomnia are usually poor and only a small group of patients might have any effect. Other therapy approach for insomnia would be better (including stress reduction, relaxation therapy, sleep hygiene, sleep restriction). But some patients prefer to drop a pill instead of a psychotherapeutic approach to change their sleeping habits or problems.
Long-time use of melatonin is not recommended, because we do not know much about long-term effects, side effects or interaction with other drugs.
There might be special indications for the therapeutic use of melatonin (delayed sleep phase syndrome), but a common use of melatonin is not recommended at the present time.
More information provided by the American Sleep Foundation with a very interesting FAQ