So, having thought about it, I was thinking about what qualifies as a weapon. Technically, anything that causes harm to an opponent could be considered a weapon...so what can cause harm?
At relativley low energies, weapons magnify force by concentrating it on a small area (slicing or piercing), or by adding weight to it (bludgeoning), or some combination of the above. Most of the classic D&D weapons fit here. Most sci-fi versions either use exotic materials for strength or other unusual properites, or replace the business end with a supertech alternative like monowire, vibrating material, or limited range energy such as a laser or gravity blade. Some high-tech melee weapons are meant to be concealed or disguised, and may be multipurpose. Still, once you have super-advanced technology, the idea of hitting somebody over the head with a club, even if it is made of vibranium, seems a bit crude.
Firearms transfer energy by shooting a small bit of metal at a high speed at the target, with effects ranging from BB stings to chunky salsa to Deep Impact. These weapons typically use air, various types of chemical explosives, magnetic fields, or even gravity waves. Alternatively, the weapon itself might be self-propelled, either via rockets, jet engines, various space drives if in space (e.g., ion drives), or anti-gravity technology. These are usually referred to as drones or missile if self-guiding. Many (but not all) carry warheads of various types of explosives. Projectiles can be in the form of darts, bullets, or even mini-black holes.
Explosives commonly come in various strengths of chemical explosives, nuclear (fission and fusion), and anti-matter. They can be guided or not, although most sophisticated munitions even today are guided. Depending upon how it works, some supertech forms of disintegration might be an "explosion." Gravity pulses might also count.
Similar to explosives are burning weapons, ranging from actual fire (flame throwers) to chemical (mustard gas and napalm) to high energy (explosives, plasma). Note that weapons that simply heat the target belong more in the category of energy weapons.
Energy weapons use electromagnetic beams (masers, lasers, x-ray lasers, etc.), particles (neutrons, etc.), super-heated plasma, lethal sonic weapons, or exotic concepts like hyper-accelerated mesons. Disintegrators are usually grouped here. Sci-fi has literally tons of these, ranging from Star Wars blasters to Babylon 5 particle cannons.
Next we have weapons that affect the target's nervous system in some fashion. These include tasers, but also neuronic whips, tasps, non-lethal sonic devices, control collars, etc. They either influence your behavior or make your body stop working (possibly temporarily). Psionic weapons are a special category of this, and could have a variety of effects ranging from control to violent death.
There are weapons that interfere in other biological processes: eating, sleeping, procreating, thinking, respirating. These tend to be either biological or chemical weapons, though with supertech you also get nanotechnology. Exotic energy fields might also apply in some settings. An alternative to interference is transformation -- into anything from a superwarrior to zombie to a pile of goo. This could happen at the individual or the ecosystem level.
Teleporters have an obvious military effect, both in terms of transport of various nasty things and in terms of stealing away something your foe needs (ammunition, fuel, body parts). Settings without some way to block teleports will likely get very nasty very quickly.
Some weapons alter the nature of reality. They might shift dimensions (technically what Star Trek phasers do in some descriptions), alter local laws of physics in various ways (e.g., make molecular bonds lose strength), introduce an element of Chaos (literally in WH40K?), or wipe something from existence (e.g., the superweapon that was destroying the universe in one of the Well of Souls books). Planet or star-destroying weapons sometimes fall into this category if they are not of the brute force Death Star variety.
Time travel weapons are a special case. Sending somebody forward in time might happen via wormhole, or only practically in the case of stasis fields. You might cause somebody to blink through time in a way that disorients, or force somebody to age rapidly. Sending somebody into the past is risky, unless your world works on the branching threads theory of time travel.
Deep enough understanding of somebody's psychology might allow you to manipulate them in drastic ways. In the Traveller universe, supposedly the Hivers were able to do this to several Centaur colonies so thoroughly that the Centaur immediately stopped the war and vaporized the colonies in question. This is less of a weapon, per se, than a capability.
Some societies might engineer their own population through cybernatics, nanotechnology, biotech, or various combinations to make individuals into weapons. This is a fairly common sci-fi theme. Animals or quasi-sentient creatures (e.g., Alien), can also be used.
I think that covers most of the ways that authors have invented to destroy, mangle, kill, cripple, or incapacitate characters.
