The risk probably depends on your age. I've flown from LAX to Hong Kong and back in business class before, and the flights leave after midnight local time. I found it no trouble to sleep for 12 hours without taking any drugs. No blood clots, no dehydration :)
Neither of us can really hope to assess the change in risk of something like DVT based on personal experience. We're talking about something that normally kills some tiny portion of travelers (1 in 100,000 passenger legs, maybe?)... if not moving around increases that risk 10x, you'd still have to do a few hundred thousand flights to know.
Edit: The annual risk of DVT apparently runs about 1 in 3,000 for the general population. So if you were a higher risk passenger (older) and flew really regularly, I could see it getting down towards say 1 in 100 annually. Even then, you'd still need decades of data to make any conclusion.
OK, but how is lying in bed on a plane different from lying in bed on the ground? (If it's the difference in air pressure, wouldn't everyone in Denver and Mexico City be dead by now?)
For one thing, when you're lying down, your feet are generally level with your heart, which makes it easier to circulate blood through your legs. Also, you're going to change position naturally while sleeping in a bed, but you're much less likely to do so when jammed into an airplane seat. Plus most people don't spend more than 8-10 hours in bed at a time, whereas DVT is primarily a big concern on long flights stretching 12-20 hours.
