What are good security tactics for sleeping in airports?

Use your suitcase/bag as your pillow, you'll know as soon as you miss it! If you have more than one bag, put your hands through the bag handle or tie it to your hand or leg when you fall asleep.

Most importantly travel light, the lighter you travel, the safer you will be!

In airports in Christian countries, I also heartily recommend seeking out the chapel. Its a nice, quiet place, where you can "meditate" in silence. (Hey, I'm also an ordained priest, and while people like my sermons, don't think I haven't seen the occasional person "meditating" even during the songs!) Its a easy place to find some shuteye, as long as you are respectful. (Also, I would check the hours and make sure you won't be there for a service!) The beauty of this is that criminals tend to avoid chapels, mostly out of guilt, so you have a relatively safer place.

Along these lines, in Muslim countries, there are also ablution fountains near the prayer halls. If you are really in need of a shower when you wake up, use the ablution fountain as a dip and pour. Remember that Muslims pray (and wash) five times a day, so be discreet and look for non-prayer times.

I find it useful to carry a light chain or a nylon strap, such as those found in backpacks (something difficult or time-consuming to cut through, enough to disturb your sleep). Wind it through your baggage limbs and then across a body part. This is quite useful for securing multiple pieces of luggage. Also, not directly related to the question - Carry a neck pillow, in case you don't have one already. You'll sleep like a baby!

One of my biggest worries when sleeping in airports is whether my luggage is safe; everything else, I don't really care. If there's a 24-hour luggage storage or a locker facility I drop off my bags there and that helps incredibly in peace-of-mind in relaxing.

Now if you're the kind who passes out cold when sleeping then things are going to be difficult for you. However, if you find you can easily take power naps then you can take that at a cafe or a restaurant. They will throw you out if you stay too long but as long as you buy something you can safely catch some sleep for 30-60 minutes. Once you learn how to take power naps, you'll find it causes less fatigue as you can catch the restful cycles of sleep without sleeping in an uncomfortable position for too long.

Hide your valuable items (if small) deep under your clothes, that way it will be hard to steal them from you (and hard to find).

You could also try to make a new friend (easy when you both are stuck at the airport) and keep an eye on each other. On the other hand your new "friend" might be a pickpocket, so use your brains.

Or if you have a lock with you, lock your bag to something fixed.

Another possibility is lockable bags. I have a couple of these for when we take train trips where the luggage security situation is much worse. Beware that bigger is not always better--the bigger the bag the bigger the holes in the mesh that someone could use to worm something small out.

They're basically a wire mesh bag with a drawstring that you can loop around something substantial and then bring back to the bag and lock. The biggest ones--which is what I linked--will hold bags as large as the airline carry-on limits.

While it's not perfect it's enough to defeat the thief intending to stealthily go through someone's bag or pick it up and pretend it's theirs. I can't think of anything that could get through it that you're allowed on a plane.

At the airports they usually have those plastic crates, either big ones to put your big bag when you checking or smaller ones that you put your things into at security check, or both.

You can grab some of these and put them upside down, side by side and form an improvised bed out of them. This serves two purposes:

1) You can put all your valuable things (if the crates are big enough) under the crates and it will be impossible to steal them while you lie on them.

2) It isolates you from the cold cold floor