It turns out to be remarkably difficult to trace the history of small squares of fabric back to an origin point. However, the word bandana has a recorded history; it was originally a Hindi-Urdu word for a dying process similar to shibori and tie-dye, and grew to mean any decorated square of fabric.
I admit, I grew up with a sort of bemused city girl snobbery about bandanas. And then I did CRM, and hiked in the woods for a living and discovered that:
The sun is hot.
I am allergic to everything.
Which is what led to me occasionally double bandaning, wearing one as a particle mask and the other to keep myself from getting one of those amazing red necks we hear so much about.
As fall rolls around us (or spring in the southern hemisphere), consider incorporating one of these handy items into your garb!
A list of ways they were commonly decorated is here. For some of their uses in the American West, see here!