I have never used any sleeping aids on trips to Europe. Maybe I am afraid I wouldn't be alert in an emergency. As for Melatonin, I bought it once, but couldn't find out if I was supposed to take it when I wanted to sleep or when I wanted to wake up, so I never took it.
IMO, the best, and, in fact, the only recourse for jet lag (or desynchronization) is to re-synch your biological clock to local time by exposing yourself (NO, not that way!) to early morning sunlight. Some accompanying exercise seems to help, too. Actually, I have found that sitting in a hot sauna or steam room early in the day can help. I think it has something to do with the warmer temperatures your body equates with midday.
None of the other remedies suggested here (sleeping on the plane, plenty of liquids, etc) have any effect on true desynchronization, although they may help reduce the effects of travel fatigue, which is another problem and may exacerbate the effects of jetlag.