Plain ol' 100% cotton cloth is a remarkably versatile thing to have around, so much so that it ranks as one of Dave Canterbury's 10 Cs of survivability. It has endless uses - from covering to absorbing to cleaning to creating char cloth - and takes up little weight in a pack.
The classic bandana is probably the most common, though I've moved away from it in my kits. The readily available bandanas are dirt cheap, but they're also made of the thinnest, crappiest cotton possible, and I find them a bit on the small side to be really handy.
Shemaghs - the Middle Eastern fashion accessory adopted en masse by troops serving in the region - have taken over the hole in my heart (and kits) once filled by the ol' bandana. Larger and made from better materials, they are superior in pretty much every way. Good shemaghs are a nicer, softer cotton that feels cozy against the
skin - important if you're using it as a scarf/hat/pillow/baby blanket (not all at the same time). The larger size means they're more functional, especially in roles like a makeshift towel, sling for an injured limb or so on.
Also, there are a great many cool shemagh designs out there than bandanas. Cool designs are very important. I buy my shemaghs off the interwebs or at gun shows, though that is where I buy most things. If you don't do some portion of your shopping at gun shows, you really need to re-evaluate your life.
The third option, and one oft overlooked, is just throwing a rolled up cotton t-shirt in your kit. In a pinch, it can do pretty much everything a bandana or shemagh can do, and it can also act as...wait for it...a t-shirt! Having a clean shirt can prove pretty handy in the course of real life, and most of us have a few oldies kicking around. Yes, nothing special and decidedly un-tactical, but sometimes practical wins. Ranger roll that sucker up with a pair of socks and you're in business.
Any of you survivalist brothers and sisters have a preference for how to pack your cotton? Tips for the masses? Don't pack any?