Flamer
The Flamer is a short-ranged support weapon employed in many different variations by nearly all of the races of the WH40K universe.
Overview
The flamer is a weapon that sprays an area with extremely flammable liquid/gas known as Prometheum (no relation to the actual element Promethium but a reference to Greek God Prometheus), burning anything in front of it. Now apart from the varying degrees of burns you'll receive when you're in the business end of one, your squad won't really be motivated when they see a giant firewave of painful and slow death and see that the rest of them are experiencing said pain and death so they'll probably run for it... unless you're fighting with anyone short of adamantium-forged testicles where they'd probably charge the gunner for vengeance.
Armies field flamers in different sizes ranging from pistol-sized flame units, a regular rifle sized unit to a fuckhueg flamer capable of bathing entire platoons in fire with a single burst. Table-top wise, Flamers are special weapons that ignores cover bonuses and extremely effective against infantry. Very good against the Tyranids due to their total lack of vehicles, so you always have a chance at hurting most any tyranid unit you shoot at, plus it's great for killing all those pesky rippers.
Imperial Variations
A cruel and painful weapon in its own right, this would not be 40k if there weren't several variations of the flamer, each deadlier than the last.
Flamer Pistol
Mainly used by the Adepta Sororitas, Hive Gangers, and the Inquisition, this weapon is a pint-sized flamethrower that can be wielded as if it were a pistol. Some extremely unhinged individuals go as far to dual-wield them for extra burny power.
Flamer
The regular sized flamethrower as described above, used by nearly everyone in the 41st millenium.
Combi-Flamer
The Orks have proven that any weapon can be made more dakka by slapping another weapon onto it. Combining this with the Imperium's love for flame weapons, the combi-flamer is a weapon that can be strapped onto a regular Bolter to allow for a single gout of fire when needed.
Heavy Flamer
The big brother of the regular flamer, able to do far more damage. Mainly used by Terminators and vehicles, they are also carried by the Sisters as a heavy weapon, by everyone in the Salamanders and by the Catachans because they simply don't give a fuck.
Flamestorm Cannon
An even bigger variation of the flamer, found on the Land Raider Redeemer as a sponson weapon and the primary weapon of the Baal Predator.
Inferno Cannon
The primary weapon of the Hellhound, this weapon focuses on the "thrower" aspect of "flamethrower". Similar in strength to the Heavy Flamer, the Inferno Cannon can project its payload over a considerable distance.
Inferno Gun
Some men just want to watch the world burn. Others provide the matches. The Inferno Gun falls under the second category. Mounted only on the Warhound Scout Titan and the Malcador tank it will do horrifying damage against anything caught in its path.
Chaos Variations
Chaos Space Marines and Daemons both use flame weapons with fire generating from more warp-derived sources. Results of this are positively deadly as fuck! Additionally, CSM use a lot of the imperial flamer variants including the flamer, heavy flamer and combi-flamer.
Burning Brand of Skalathrax
Rumoured to be the weapon employed by Kharn himself to burn out his allies for being faggots and shying away from cold weather on Skalathrax, the Brand has a colourful history of burning shit to death - most notably power armoured Mary-Sues. This is a unique weapon that projects a gout of Khorne's (or Tzeenetch? Nobody knows exactly) best fire at a long distance, to chase out and scorch anyone who might be hiding in cover.
Baleflamer
A larger, more common and much deadlier flamer that takes the Flamestorm Cannon one step further - in that it shoots further! These are exclusively seen on CSM Helldrakes and are super effective against almost anything NOT wearing terminator armour or hiding in a BIG METAL BOX.
Breath of Chaos
Employed exclusively by Daemons, this is less of a weapon than it is a shooting attack - a shooting attack that eats through armour, body and spirit with ease, that is. Effects of this weapon are as varied as the Changer of Ways himself, but can include anything from simple conflagration up to fire that turns things into tentacles or frogs or - well, we can't really make an accurate assessment of this attack. Seen used by Flamers of Tzeentch mostly, but also by Daemon Princes and Lord's of Change.
Alien Variations
Though the Imperium has by far the most flame weapons, certain aliens also employ them.
Eldar Flamer
Used by Storm Guardians to support their role as close-quarters combat and by Wraithlords as secondary weapons for assault-oriented constructs.
Dragon Breath Flamer
Used by exarchs of the Fire Dragons, these weapons can sear anything that gets within range of their wielder.
Ork Flamer
The Orks employ Burnas for their flamer-duties. These weapons are unique because they can also be used as cutting torches to deal serious damage in close combat. They are also essentially a burning gas-can, strapped on a stick, to give you a hint on what they usually look like.
Tau Flamer
Used soley by Crisis Battlesuits, they are meant to deter close-range attackers. Due to the nature of said battlesuits, they are not intended to be used as a primary weapon.