Melatonin gives me the "vivid dreams" (i.e., "what-the-hell-was-THAT-all-about dreams") side-effect, but really doesn't help me with jet lag. A couple times a year I fly from the east coast US to Thailand, which is a night-is-day day-is-night time difference, I sleep very little on the flights over (not by choice).

When I get to Thailand I just stay up until the local time for sleep is appropriate, then pop a 5mg Ambien. I do the same thing for the next 3 or 4 nights, and after that I'm pretty much adjusted to local time. On the return, I may take a pill the first night I get back to the US, but after that I adjust quite quickly when I have my own bed and shower. I used to not take any medicinal aids on principle - and spent many nights sleepless nights. I finally decided the hell with it and made Ambien my travel buddy.