Granted, this one is not very exotic, but at least it's not well known and well-understood any more, since the bow has absorbed the sling's place as ancient ranged weapon in our memories.
The sling was used in many parts of the world, but the Rhodian and Balearic mercenaries were most feared in the ancient Mediterranean world because of their expertise in employing slings (as were the Cretes due to their bow skills and the Spartans due to their heavy infantry skills). The construction of a sling does not require much (it's a piece of natural rope with sometimes a piece of leather to fix the projectile). It could be worn as a head band, around the waist, around the neck, in pouches - everywhere. It's most probably the lightest but successful weapon ever. Its dangerousness exceeded that of most ancient Mediterranean bows, but it depended a lot on its projectiles. You could just carry the sling with yourself and pick up stones on the battlefield, but then you'd have a rather limited performance. Still nasty, but not exceptional. Using well-shaped and well-sized stones yields better results. Dedicated lead projectiles as they were used by mercenaries whenever possible were extremely deadly. Anyone who uses a sling as recreational activity today is strongly advised not to use golf balls - it's simply too dangerous.
The late Roman empire's author Vegetius advised the Roman emperor to have this cheap, lightweight weapon as standard (alternative) weapon for all soldiers - its usefulness easily exceeded the effort of carrying it and exercising with it:
Recruits are to be taught the art of throwing stones both with the hand and sling. The inhabitants of the Balearic Islands are said to have been the inventors of slings, and to have managed them with surprising dexterity, owing to the manner of bringing up their children. The children were not allowed to have their food by their mothers till they had first struck it with their sling. Soldiers, notwithstanding their defensive armor, are often more annoyed by the round stones from the sling than by all the arrows of the enemy. Stones kill without mangling the body, and the contusion is mortal without loss of blood. It is universally known the ancients employed slingers in all their engagements. There is the greater reason for instructing all troops, without exception, in this exercise, as the sling cannot be reckoned any incumbrance, and often is of the greatest service, especially when they are obliged to engage in stony places, to defend a mountain or an eminence, or to repulse an enemy at the attack of a castle or city.
The sling is probably the oldest weapon still used in modern warfare, as it's in use with Palestinians and other low combat intensity fighters (the dagger is about as old if you consider flintstone daggers). Back in ancient times, it was always a wise choice to carry a sling simply because it was no real burden at all, but quite useful at times.