I've got a few shemaghs in different colours, weights, designs...probably one of the most useful items of clothing someone can own.
In addition to the other suggestions above, I've worn one as a sarong when waiting for gear to dry, used it rolled up to carry gear, an impromptu carrier for foraged items a quick dog lead' for stray dogs, for a windbreak for one side of a shelter.
Can be used for a variety of first aid applications (similar to a scout 'neckie').
You can stick a rock (pile of gravel or even soil) in one to attach to a rope if you need some weight on the end for distance/height.
A quick & easy storage device when sleeping under a tarp, natural shelter or hammock.
Keeping dreaded Scottish midges off your face & neck...especially when covered in repellant.
I quite often use one to lay on the ground when taking stuff out my pack/pockets as a way of ensuring you don't lose stuff...and when doing food prep in the field (I'd rather lift dropped food off my shemagh than the ground)
It's also a handy item for wrist/arm/leg locks...great fun to teach & practice with my kids...although my wife keeps complaining about the noise & general mayhem that comes with it