Metaphorically, anything used to damage (even psychologically) can be referred to as a weapon. Weapons can be as simple as a club, or as advanced as a nuclear warhead.
For a comprehensive list of weapons and doctrines see military technology and equipment.
A widespread early weapon, perhaps finally understood, is the "stone handaxe." This is a flat, sharp-sided stone disc, with an egg-shaped or triangular projection. Some paleontologists built one and threw it, and noticed that it lands with the pointed edge digging into the ground. They believe that it could be a "killer frisbee" to harvest animals from a tightly packed wild herd.
The crucial weapon that appears to have given humans superiority to animals was a lightweight flexible lance with a broad-bladed stone head (flint chert, or obsidian). This lance was usually thrown from a spear-thrower.
This weapon probably killed the giant sloths and elephants. Modern versions of these devices remain within the living memory of arctic tribes to hunt whale and walrus.
When thrown from a spear-thrower, a lever to extend the arm, the lance bends, storing energy, and then straightens. It then strikes animals at effective ranges to over thirty meters. The range is definitely limited by aim, not power. Anthropologists constructing lances and throwers have thrown lances through several inches of oak. The broad, leaf-shaped heads penetrate deeply, and cut arteries well.
Archery and swords have been crucial for warfare. Archery, because of its firepower, short swords because of their lethality in close combat. The most effective defense to these was a fortress. The doctrines to support fortresses in the age of edged weapons may have caused much of medieval and noble history. Of course, medieval siege weapons were used in countervailing doctrines.
During the 16th century to 19th century firearms became increasingly important and effective. During the U.S. Civil War various technologies including the machine gun and ironclad ship emerged that would be recognizable and useful weapons of war today, in lower-tech regions of the world. In the 19th century warships shifted also to use of fossil fuels and were no longer dependent on sail.
The age of edged weapons ended abruptly just before World War I with rifled artillery, such as howitzers which are able to destroy any masonry fortress. This single invention caused a revolution in military affairs and doctrines that continues to this day. See military technology during World War I for a detailed discussion.
An important feature of industrial age warfare was technological escalation - an innovation could, and would, be rapidly matched by copying it, and often with yet another innovation to counter it. The technological escalation during World War I was profound, and produced armed aircraft, the hand grenade, and the tank.
This continued in the interim period between that war and the next, with continuous improvements of all weapons by all major powers. Most modern weapons of war are mild improvements on those of World War II. The aircraft and tanks are faster, the rifles lighter, the artillery more mobile, the radios more reliable, but they would all be recognizable to any soldier of that era. See military technology during World War II for a detailed discussion.
In modern warfare, since all redoubts are traps, maneuver and coordination of forces is decisive, overshadowing particular weapons. The goal of every modern commander is therefore to "operate within the observation-decision-action cycle of the enemy." In this way, the modern commander can bring overwhelming force to bear on isolated groups of the enemy, and tactically overwhelm an enemy. See military technology of the late 20th century.
Traditional military maneuvers tried to achieve this coordination with "fronts" made of lines of military assets. These were formerly the only way to prevent harm to friendly forces. Close-order marching and drill (a traditional military skill) was an early method to get relative superiority of coordination. Derivative methods (such as "leapfrogging units to advance a line") survived into combined arms warfare to coordinate aircraft, artillery, armor and infantry.
Computers are changing this. The most extreme example so far (2003) is the use of "swarm" tactics by the U.S. military in Iraq. The U.S. had instantaneous, reliably encrypted communications, perfect navigation using GPS and computer-mediated communications to aim precision weapons.
In swarm tactics, small units pass through possible enemy territory. When attacked, they try to survive, and call down immediate overwhelming showers of precision-guided air-dropped munitions for armor, and cluster bombs for enemy troops. To consolidate such a region, nearby artillery begin bombardment, and ground units rush in on safe vectors through the bombardments, avoiding them by computer-mediated navigation aids.
Thus in modern warfare, satellite navigation systems and especially computers create decisive advantages for ordinary military personnel with weapons that are serviceable, but otherwise unremarkable.
See also riot control agent, non-lethal, weapon of mass destruction. Netwar contains a discussion on using information technology as a weapon - more commonly called information warfare. See also persuasion technology and propaganda for discussions of the way information technology plays a role in the changing of the minds of subject populations - both branches of psychological warfare.