If sleep and time (and melatonin) haven't helped, find a distraction from the upside down travel time.
1. Get high.
In the literal sense. Put your bags down, head outdoors and find the highest point - in Cairo, the top of a pyramid, in San Francisco, Coit Tower, New York, The Empire State, back in Auckland, the Sky Tower. Get some air, orientate yourself with the views and be assured you're alive, if a little sleepy.
2. Go shopping.
Some people find there's nothing like a spot of shopping to get the blood pumping, the thrill of chasing a bargain or spending too much money. And if you've returned home, simply restocking the cupboards is satisfying because, when you do pass out, you'll want to wake up to something to eat.
3. Stay awake.
Try to stay awake at least till a reasonable approximation of bedtime, however much you wish to close your eyes. It's hard to sleep when you're eating, so head to the food markets, specially if you're somewhere exotic, and try the eels in aspic, or deep fried scorpions.
4. How about a spa?
If it really is all too much, you can always take the indulgent path and limp to the nearest spa. Waxing is guaranteed to keep you awake till bedtime, eyebrow plucking ditto, or just get a massage and hope you don't snore.