As you will probably arrive in Europe in the morning hours, you should make sure that your hotel can accomodate you before the regular check-in hour. While sleeping will not help to get in sync with the new timezone, it's nice to get into your room, take a shower, and give the day a fresh start.
Depending on where you start your trip in the US, your inner clock will still be set to 2 or 3am when you will arrive in London with a flight that starts in the evening in New York.
Don't overdo your sightseeing on your arrival day and allow yourself some leisure time to adjust.

Seriously, Cowboy - save from paying for an extra night, no hotel will guarantee they can give you a room early in the morning. Every hotel will say they'll give you a room if they have ones available, but nobody will guarantee it.

I always reserve the hotel the night of my departure to Europe. It is worth it to us to be able to get in our room immediately to shower, change and just relax for an hour or two.

Seat etiquette in <s>cattle</s> I mean coach class is also important: http://www.news.com.au/travel/galler...8089357?page=1

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Vic's travels: http://my.flightmemory.com/vogilvie

I use Tylenol PM. It gives my back a little help with aches and pains and is just enough to let me zone out and sleep without being drowsy. I take two blow up neck pillows -- one for my neck and one for my back. I have an IPod loaded with "gentle rain" and waves crashing on a beach and birds sounds, etc. I find they cancel out everyone and help me sleep. I also find that a foot rest makes a huge difference. I just pull out my rolling carry on after take off, flip it sideways and use it as a foot rest. That slight change of angle, really saves my back. Oh.....and like others, an aisle seat is a must for me.

Best way to London...take the morning flight. Leave NYC at 8:30 am, arrive in London 8:30 pm, check in, go to sleep.. No jet lag.

Ditto the morning flight to London. Love it.

I download my ipod with books and podcasts. They often lull me to sleep and if not, it's restful to close my eyes and listen. I haven't had much luck or comfort with travel pillows and I've tried several for long haul trips, but my ipod is the best thing going for me. My new ipod uses a lot of battery with pictures and sometimes I worry that I won't make it through 20 hrs of travel, but so far its charge has carried me through.

A lot of good advice here, but I think Leanna has it properly summarized.

I carry nose spray to prevent the irritation from the extremely dry cabin air. My BB earbuds go in and stay in for the whole trip. They can be plugged into the BB for my personal music or plugged in to the ship's system for movies. The BB is powered by bringing my car charger adapter for the seat's power port.

I always carry a book and a couple of magazines to pass the time. I find it tough to watch the airline's programming on long trips.

Finally, janisj brings up a good point. On my first trip to China, I had an debilitating Ambien reaction that caused me to suffer much more than losing a few hours of sleep. A common complaint with OTC melatonin is the drowsy hangover that may last after you land. If you are going to try drugs, it is best to experiment before you fly.

I'm back after a fairly uneventful flight there and back. I didn't get to pack the sleep aid, the pashmina or the headphones as the transportation came way too early. Luckily, the flight there was pretty empty and I had a 3 seat row to myself. I took a travel sickness tablet (I have tried this one before) and had a small bottle of wine with the meal. I arranged the small pillows and the blankets to cushion the armrest and had about a 4-5 hour sleep in a 9 hour flight with not many interuptions. I felt fine getting off the plane in London and had another 2 hour flight after that.
The flight back was a bit different in that when I checked in online at less than 24 hours to go, there was a lot of empty seats available, not so when I got on, it was a full flight. I think other flights might have been cancelled and the passengers put onto our flight. The Bonine and wine worked again this time, but only a 2-3 hour doze. Thanks again for all your helful replies. I hope it helps someone else with the same concerns.

joto, soumds like you did great with that much sleep time!

Thank you for getting back to us, joto, letting us know your experience.