Chainsword
The Chainsword is a fuck-awesome melee weapon, heavily used by Imperial forces, although variants are fielded by the Eldar, Orks, Chaos Space Marines as well as just about any fucking imperial assault troops.
Apparently in the 41st Millennium, chainsaws have been repurposed for hacking down things/aliens/people instead of simply harvesting lumber.
As its name implies, the chainsword is a bladed weapon with a rotating chainsaw blade in-between, that's powered by a motor mounted on the hilt and activated with a trigger on the grip. Of course, the sheer manliness in this weapon makes it pretty damn heavy, so it's actually really fucking impractical awesome. But since almost all the users of it have some combination of power armor, bionics, or natural strength to swing them around, the weight is a lot less of an issue.
Although the chainsword is issued to virtually all forces of the Imperium, it is most famous with the Spehss mahreens who widely use the chainsword as the primary weapon of their assault troops and veteran soldiers, although the standard chainsword has the same rules as any other close-combat weapon.
Variants
The Chainsword also has several variants that have been developed by both the Imperium of Man and Xenos. Here are some examples:
Eviscerator
An oversized chainsword used by the Ecclesiarchy's priests and by the Sisters Repentia of the Sisters of Battle (as well as Chapter Master Gabriel 'IN THE BALLS' Seth). Most recently however, Eviscerators have found their way into the hand of 7E assault marine sergeants, because meltabombs just weren't enough. The Eviscerator is twice the size of a regular chainsword and so heavy that a normal soldier will need to wield it using both hands. The Eviscerator might also incorporate an exterminator, a portable flame unit that will not only help it breach armor, but also scare the fuck out of any normal man upon seeing a whacked up priest/nun swinging a fucking huge flaming sword-chainsaw. The Eviscerator is also extra effective against armored units.
Scorpion Chainsword
An Eldar variant of the Chainsword fielded by the Striking Scorpions. It's like the Imperial Chainsword but incorporates advanced equipment that increases the wielder's strength and incorporates a sleeker, less bulky design. There's been fluff that suggests they are actually a lot more advanced than Imperial chainswords, consisting of a heavily serrated 41st millennium mono-molecular blade which doesn't whirl around most of the time. Rather, upon hitting an opponent, and the blade gets stuck in their body/armor, THAT's when it goes all chainsaw, ripping armor and people apart and ensuring that the blade doesn't ever get stuck in someone; it'll either go through them or at least rip whatever it's stuck in enough to be pulled out.
Exarchs can use two variations of the Scorpion Chainsword: the Biting Blade (a massive two-handed weapon whose effectiveness increases as a target is hit), and the Chainsabres (two one-handed chain weapons that can land a truly staggering amount of blows on a target).
Chainaxe
Yes, Warhammer has chainsaw axes, as insane it sounds. The custom weapon of Khornate champions, the Chainaxe was a fairly common weapon among Imperial troops pre-heresy. It's basically a huge axe with a powerful chainsaw as a blade. The sheer weight of the axe and the fact that most Khorne Chaos Marine champions are super strong and completely fucking nuts ensures these will tear through most infantry armor. It's wielded by non-Khornate Chaos Marines as well, due to the greater damage it inflicts. Pre-heresy it was practically standard issue among the World Eaters. Among Imperial forces, a chain-axe is most likely to be seen in the hands of a Space Wolf or a Raven Guard - the former due to the fact that they just don't give a flying fuck that it might associate them with Chaos, and the latter due to the fact that they mostly have older equipment due to infrequent resupplies. They are also very common among Flesh Tearers because they basically already are a Khornate cult.
Chainglaive
The Chainglaive is an evolution of the Chainaxe, giving it a longer blade and haft allowing for wide, sweeping strikes capable of rending power armour without much trouble. It's used extensively by Vanguard Marines and Chaos close-combat specialists. An ancient design by modern standards, it's by no means common, and sees use primarily with the traitor legions due to this (particularly with the Night Lords, who had always favored its use).
Chainscythe
Seen wielded by the Spyrer Matriarchs, this variant of the chainglaive mounts the blade at a horizontal angle to the tip of the shaft.
Chainhammer
Chainaxe not insane enough for you? Black Crusade introduces the chainhammer, a massive maul outfitted with multiple rows of spinning metal teeth on the club-like head, which rip apart flesh pulped by the brutal impact of this insane weapon.
Chainspear
Similarly to the chainglaive, this weapon combines reach with lethality, mounting a chainsaw-bladed length at the end of a long haft, ensuring that jabs and thrusts can tear open flesh with the lightest touch whilst keeping the wielder out of harm's way. According to Tome of Blood, some variants actually sport the sharpened teeth of the bearer's former victims as the cutting edges.
Ironfang Chainsword
A variant of the chainsword created to allow human heretics to approximate the deadly blows of a Legion chainsword, this variant features a thick, bladed area with chained teeth nearly twice the width of an ordinary chainsword, and powered by a backpack-mounted fuel supply. Its greater tearing strength and weighted nose allow it to deal viciously violent heavy slashing blows. Needless to say, this weapon is heavy - 12 kilograms in weight, complete with power supply - and unbalanced.
Chainfist
Intended for Terminators involved in boarding actions, the Chainfist is a Power Fist that incorporates a powerful chainsaw blade for the purposes of slicing through armored bulkheads. The weapon is commonly used by Terminators as a CQC weapon, and to rip the armor off Space Hulks during boarding actions. Because it can penetrate thick metal with little trouble, it's often used for ripping open enemy vehicles and bunkers.
The reason it's so effective is simple. The powerfist's energy field also encompasses the chainblade. That's right, the chainfist effectively marries a chainsword and powersword. That's just plain scary. But it doesn't make the least bit of sense of why it's better than a power sword in the first place. The molecular bond destabilising powerfield weakens the target. Then the teeth of the chainsaw blade tear that substance apart. The alternative is having a static piece of metal that is still cutting, but just not as efficiently.
Chain Choppa
The Chain Choppa is the Ork version of the chainsword. The weapon is a handheld chainsaw (though it sometimes takes the form of a sword or axe) used for almost anything. Really, you name it. In a pinch it can stand in for anything ranging from a weapon to a household tool. While choppas of regular Ork boyz rarely have these weapons, while richer Orks like the Warboss or a Nob might have it because it's killy and flash. Many are simply war trophies picked up from loyalist and traitor Space Marines.
