A bandana is probably the most usefull bit of gear you can carry for such light weight.
They make a handy container if you suddenly find yourself with a handfull of small objects with no container, like a handfull of cartridges, some nuts and bolts, large amount of change. Or a handfull of pipe tobacco a friend is giving you out of his humidor to take home and try.
I've used one as a coling device on a hot day out in the boat. dip it over the side and tie it on your head pirate style and let evaporation do its job.
Used in a similar way it has kept my ears frome freezing when I was out on an unexpectedly long time in bad weather. I folded it into a triangle and tied it around my head, again pirate fashion, with the material over my ears, then put my ball cap on over it. That layer of cotton kept my ears safe from the cold snow that was comming down, and the extra layer of doubled over material under the hat kept my head a bit warmer.
It makes a decent presure bandage in a pinch.
Rolled up in a tight band it can be used to tie something together, like the time a set of car keys got dropped through a storm sewer grate. We could see the keys about 6 feet down. A long branch was cut from a nearby tree, part of it out at the tip was bent over and broken and then tied at a 45 degree angle so the keyring could be "hooked".
In a pinch you can cut it into long strips to make a long something to tie something else, like splints on a suspected broken limb.
Folded up in 4's it makes a passable pot holder to get the coffee pot off the fire.
Working on some things when doing house projects it's made a decent dust mask, keeping the spackle dust out of my lungs.
A million and one things.
if you absolutely have to, you can always wipe your nose with it.
I always keep two on me. One is folded into 4's and then rolled up and placed along the outside of my right hand pocket. This keeps you pocket knife and AAA flashlight standing up in the front part of your pocket more comfortably. The other is folded up and goes in my back right pocket for "just in case".
Once you carry one for a while, you'll never be without one.