Force Weapons
Force weapons are psychic weapons in Warhammer 40,000, used by the Imperium of Man, Chaos Space Marines, and the Eldar. They are used almost exclusively as close combat weapons by psykers, and serve to store up and channel psychic energy. Force weapons are very useful against Daemons, as Warp energy is one of the few surefire ways to put down a Daemon. They are, in most cases, not explicitly power weapons, although the difference is usually negligible to those on the receiving end.
The only army that uses force weapons as near standard issue equipment pieces are the Grey Knights. They can also have ranged "force" weapons, such as the Psilencer and its Dreadknight counterpart, the Gatling Psilencer.
In 8th edition, generally bump a weapon's damage to d3. Previously, they had a psychically-activated Instant Death. In the role playing games, they tended to kill everyone, including the user, but that was true of most psychic powers.
Imperial
Force Staff
Serving as a conduit for psychic energy, force staffs are used to channel the wielder's psychic power through the staff and direct it at an opponent, usually in the form of warp fire or warp lightning. Clan Raukaan has one that acts as a thunder hammer.
Force Sword
Like the force staff, a force sword gathers the wielder's psychic power, but instead of channeling it at an opponent, it will store the accumulated psychic power as warp fire coursing along the blade, allowing the psyker in question to attack his opponent with a flaming sword.
Force Axe
Like the force sword, but as an axe.
Nemesis Force Weapon
Nemesis force weapons are the signature weapons of the Grey Knights Space Marine Chapter. Made of special materials containing iron and silver, the power of a Nemesis force weapon is proportional to the Grey Knight wielding it. Additionally, Nemesis force weapons are one of the few types of force weapons that are also power weapons. The most common types are Nemesis force swords and Nemesis force halberds.
Furioso Force Halberd
Furioso Force Halberds are basically Dreadnought sized force weapons used by Blood Angel Librarian Dreadnoughts.
Psilencer
One of the few available ranged Force weapons.
Psilencers are a type of psionic weapon created by an unknown Xeno race and made use of by the Grey Knights Chapter. Whether the technology was stolen or freely given to the Grey Knights is not known; all that is known is that it is unlike any weapon within the armories of the Imperium.
They function by channeling the psychic might of the user where it is not only focused but amplified. The unique design means that it lacks a triggering mechanism but instead the wielder channels his psychic might into the containment core of the weapon - after which, focusing crystals channel the resultant energy into a refined azure energy pulse capable of destabilizing the physical form of a Daemon.
On the 7th ed tabletop, it is pretty underwhelming despite the cool fluff; being a gatling gun that fires off six shots a turn at strength 4 at AP-, so daemons with armor will shake it off and even Orks get saves against it... at least, until you learn that you can use Force on this. If you're fighting a lot of multi-wound monsters, you are spamming Psilencers; their precious plot armor can only protect them for so long. Still, this is still a S4 weapon, so you aren't looking to go one-on-one with a Greater Daemon. What the Psilencer is better for is killing swarms or multiwound infantry, or for denying Feel No Pain. Of course, then it is competing with the Psycannon and Incinerator, so competition is high.
On 8th ed, the new psychic stratagem called Psychic Onslaught makes Gatling Psilencers, Psilencers and regular and Heavy Psycannons absolutely brutal towards regular infantry and can even scratch high Toughness models due to number of shots it can shit out. For the Psilencer, it has been buffed in 8th ed. It is now Heavy 6 S4 AP0 D1d3 gun that fires the condensed psychic power of its wielder. Literal mindbullets. Deals 1d3 damage, just like all force weapons. Now that standard weapons like bolters no longer have AP, the lack of AP on this thing stings a lot less; with 6 shots apiece, not to mention having an easier time wounding tougher models, you're sure to force some failed saves eventually. Of course you still have to be cautious to any unit with Toughness 5 or higher and a 3+ save.
Gatling Psilencer
The Psilencer on Crystal Meth. The other available ranged Force weapon.
A Gatling Psilencer is far more powerful version of the regular Psilencer. Far too large for a single Grey Knight, it is reserved for the infamous baby carriers known as the Nemesis Dreadknight. This is used for those extra large Daemons that just won't die in a single barrage of mind bullets and holy promethium. The mechanics of the Gatling Psilencer is similiar to its smaller kin, but obviously mounts more barrels and a larger focusing crystal for even bigger mind bullets.
On the crunch (7th ed), it is basically similiar to the regular Psilencer but it pumps out 12 shots with Force, making it more Dakka and more chance to mulch swarm armies. Unfortunately, despite the increase size, it is still only a S4 AP- weapon.
On 8th ed, the new psychic stratagem called Psychic Onslaught makes Gatling Psilencers, Psilencers and regular and Heavy Psycannons absolutely brutal towards regular infantry and can even scratch high Toughness models due to number of shots it can shit out. The Gatling Psilencer like its smaller sibling has been buffed due to the fact that bolters no longer have AP.
Eldar weapons
Witch Blade
The most common Eldar Force Weapon and the most recognizable.
Used by Eldar Seers, particularly Farseers and Warlocks and based on a long sword archetype, Witch Blades (or Witchblades) serve as Force Swords with a crystalline, helix shaped force crystal that is powered by the wielder's psychic power.
Used to enhance and unleash the latent psychic power of the wielder, Witchblades are effective against all infantry targets; humanoid, xenos, beast or Daemon.
Singing Spear
A Witchblade on Viagra.
A Singing Spear is a force spear which will store psychic energy derived from an Eldar Seer, which the Seer will then throw at an opponent. Once it has struck its opponent, the Singing Spear will return to its wielder like Predator.
Singing Spears obviously take the form of a long spear, thus providing greater striking range and penetrating power. However, since a Singing Spear is a two-handed weapon, its use in close combat is reduced.
Psychic Lance
The largest force weapon known by the Eldar and possibly the largest force weapon to date.
Psychic Lances are a type of Titan Close Combat Weapon with a short-range attack used by Eldar Knights. However, a larger and more powerful variety can be found on the fabled Warlock Titan.
The Eldar psychic lance uses a short burst of psychic energy directed through a crystal mounted in the Knight's/Titan's visor. The resonance set up in the crystal acts to wipe out aggressive instincts from the creatures in its area of effect. This weapon was originally used by Exodites to pacify local wildlife, but the effect can be amplified to launch devastating assaults on the minds of sentient enemies.
It also looks strangely phallic in appearance. Like a dildo with warts. Actually, fuck that, that just sounds nasty.
Eyeburst
Think of this as something like the Dark Eldar version of the Culexus Assasin's Animus Speculum...but even more edgy (Which is quite the impressive feat mind you).
The weird helmet looking thing found on Medusae. A Medusae can open its host's steel visor and paralyze those under its gaze with a wave of raw anguish, plunging them into a coma from which there is no recovery. It is unknown what the Dark Eldar would do with these comatose bodies, unless they specifically have some techno-bullshit that can bring these victims out of their deep sleep and into a surprise party.
Also, they may or may not be responsible for feeding the Medusae some psychic brain fruit. Trust us, it gets even weirder afterwards.
On tabletop, the Eyeburst used to be a rough analogue of a Flamer, which should be unsurprising since it has always been described as shooting a 'wave' of psychic terror. But with 8th edition, it is oddly not a Flamer anymore, the Eyeburst of the Medusae has 4 shots S4 with AP-2. Burns through armor well enough, but keep an Archon close for those rerolls to Hit because this thing does NOT hit automatically.
Tormentor
A very weird weapon, but its Dark Eldar so you shouldn't be that surprised.
The final training of an Incubus is to kill an Aspect Warrior and take his/her spirit stone. Said stone will then be used to make this thing you see here attached by the chest plate. A Tormentor unleashes a torturous neural wave that is, unsurprisingly, extremely painful (Hint: it involves blood being boiled). A Bloodstone is a more powerful kind of Tormentor which is made from the spirit stone of an Exarch.
Don't tell us how this shit works though.
Unfortunately there are not rules for this weird piece of weapon.