How do I prevent my head from drooping while trying to sleep on a plane?

I haven't tried this method, but it's what immediately came to my mind when I saw this question:

I have been known to use a neck pillow backwards - with the gap behind my head - or sideways, to prevent just this problem. But the best prevention is not to be entirely on your back. Turn a little in your seat so that your ear (or better still your cheekbone) is on the seatback, and your chin will not head towards your chest.

I'm a little surprised that no one has already mentioned this, but getting a window seat and leaning against the side of the cabin is helpful for overcoming this situation, since it allows you to have a more reclined angle for sleeping. Of course, this will depend on the aircraft. It works much better in a big, wide-body jet where the walls are a reasonable approximation of vertical than it does on tiny regional jets where the curvature of the cabin causes it to protrude inward at head level. I've done this many times on 737-size and up aircraft, though. It works reasonably well. An added bonus is that you don't have to lean your seat back much (or at all,) which will be appreciated by the person behind you on densely-packed domestic or regional configuration cabins that don't have much seat pitch. That part doesn't matter as much on long flights where everyone is expected to lean back (and which usually have accordingly-larger seat pitch,) though. The biggest downside to this is probably turbulence. The side of the cabin doesn't have as much isolation to dampen turbulence as your seat has, so you'll definitely feel that more. I usually try to use a pillow or folded up blanket between my head and the side of the cabin to help dampen the turbulence (and to keep from hitting my head on the side of the cabin in the event of more severe turbulence.)

Barring that possibility, in aircraft that have adjustable headrests that fold out on either side (or which have permanent protrusions on either side,) I've found it helpful to sit somewhat diagonally in the chair with my head turned to the side, so that the side of my face is laying on the back of the headrest and my forehead is held from falling forwards by the side protrusion of the headrest. Of course, make sure that you don't turn your body so far to the side that your legs are encroaching on someone else's space, though (this limitation prevents me from turning very much, since my legs are relatively long.)

Of course, the best solution is to get a seat that lies completely flat in business or first class, but I'm guessing that's not an option for most people looking up answers to this question (and usually isn't an option for me, either.)

I have no personal experience, but the first thing that came to my mind when reading this question was this:

You may buy it from here. It is called Ostrichpillow by studiobananathings.

On short haul flights I put the tray table down lean over and rest my arms on it to use it as a pillow not overly comfortable but I usually manage an hour or so of sleep.

You may wish to consider a pillow that is designed to let you lean forward into the tray table area while you sleep rather than reclining backward. One popular such option would be the Skyrest Travel Pillow from the SkyMall catalog. If you are short-torsoed, you might even be able to simulate such by simply rolling a jacket up into a ball on the tray table.

There's also something called the Embrace Sleep Collar that gives some support under the chin, butit still doesn't keep your whole head-shoulders area from slumping forward. When I travel I usually use it in conjunction with a strap around my forehead wrapped around the back of the head rest (just like Ilmari's idea). I know I look ridiculous, but sleep is sleep!

It's especially hard for short people to sleep on buses and planes because most seats are contoured for taller people, so our backs are forced into a hunched position and our heads and chins fall downwards no matter what! Btw I tried the Sky Rest Pillow also, and it was very good. The only criticism I have is that it didn't breathe (because it's made of soft textured vinyl) and it smelled plastic-y. But it is nice because it is deflatable.

My next project is to buy a Travel Halo and attach velcro to the back pillows, while also having a velcro strap around the seat. Lean back so my head is basically velcroed to the seat, and voila...? Anything to keep the head back! You might try this too. Good luck!!

Some kinds of neck pillows include a fastening mechanism, so part of the pillow prevents your head from drooping.

A flight blanket worn as a scarf (folded in half and tucked through the loop) with the loop in front can often help. It will also keep your neck warm.

You might have Dropped Head Syndrome (also called Floppy Head Syndrome and Head Ptosis). It's a condition that involves weakness of the back-neck muscles. You might want to talk to your doctor about it. One of the best non-invasive ways to prevent your head from dropping forward due to this syndrome is by wearing a plain old neck rest whenever there's a risk/chance of sleeping in a seating position. I hope this helps, good luck.

Note: Please beware of improvised wrappings and anything that could suffocate you while sleeping.