Stormtrooper
Stormtroopers are named after the WWI German soldiers who were trained for the job of rushing trenches. This meant running directly into the crosshairs of dudes who had 90% cover, and keep running, until whoever of your squad is left will fall into a 5' ditch and fight elbows-and-knees in spaces too small to swing your arms. Balls of steel, or cannon-fodder idiots, hard to tell the difference. Also called "shock troops" or "fireteams" because their purpose is to shock the hell out of the other guys by running into fire.
Thinking these guys are the same as their Star Wars equivalents will teach you a quick and decisive lesson in getting your ass kicked.
Warhammer 40k
The elite of the Astra Militarum, and the core of the Militarum Tempestus or the Tempestus Scions (also known as Stormtroopers) are the best general-combat infantry that the Imperial Guard can field, and are the toughest, best-equipped, and best-trained soldiers available to an Imperial commander that isn't a SPESS MEHREEN. They're one of only three infiltrators the Guard gets, and one of only two deep strikers (other being Guardsman Marbo) Sorry, along with the name 'Stormtrooper', infiltration is gone for them. While most of the Guard is armed with your typical angry flashlight and Flak Armor or Flak Vest, Stormtroopers normally pack Hellguns capable of astounding volleys of las fire. Though now they pack Hotshot Lasguns, which fire much more penetrating shots that are capable of piercing most infantry armor with ease, and they are clad in Carapace Armor, which gives them substantially higher survivability on the battlefield.
In earlier editions of the game, they were favored as "Light Marines," since they had fairly similar performance to Space Marines but cost considerably less due to their weaker gear. As of the new edition, they're now a dedicated elite choice, with all the pros and cons that implies. Unless you use their new codex, of course. Then they become troops.
There are many different types of stormtroopers, all depending on their homeworld. Cadia for example fields Kasrkin, Armageddon fields Steel Legion Stormtroopers, Death Korps field Grenadiers, and the Harakoni Warhawks are made up of only stormtroopers. The Inquisition also fields their own branch called the "Inquisitorial Stormtroopers", who form one of the Inquisition's main armies, the other one being the Sisters of Battle. Regardless of their appearance or gear, they're all incredibly potent if used correctly.
With the exception of the Kasrkin (and proably Death Korps Grenadiers, since dead men don't care for glory), who are revered and respected amongst Cadia, the average Guardsman in the street can't stand them, referring to them as "glory boys" and resenting the fact that they're a good deal less likely to die given that they're given better equipment than standard issue cardboard armor with a flashlight. This is likely due to the fact that Kasrkin are way more badass. Do they need some fancy carapace armor? F̶u̶c̶k̶ ̶n̶o̶,̶ ̶t̶h̶e̶y̶ ̶p̶r̶o̶u̶d̶l̶y̶ ̶w̶e̶a̶r̶ ̶t̶h̶e̶ ̶s̶t̶a̶n̶d̶a̶r̶d̶ ̶F̶l̶a̶k̶ ̶T̶-̶s̶h̶i̶r̶t̶ ̶ Umm..they use standard carapace armor like every other stormtrooper. (although they do get a fancy visor helmet). They also strongly believe that THIS WILL BE DA DAY UF GLOREE.
In Dawn of War
Kasrkin (The stormtroopers of Cadia) are available for the Imperial Guard starting in Winter Assault, and they're one of the better choices the Guard has. They suffer the same problem that almost every unit in Winter Assault has, however, in that they're redundant - they utterly replace Guardsmen by Tier 3 in that game, and in every game of WA that makes it that far, your sole mission objective from then on is to spam Kasrkin endlessly.
In the later games - Dark Crusade and Soulstorm - their numbers were hardcapped, ergo ensuring that you can only use one squad at a time.
Also made hidiously OP after Dark Crusade's infamous moving debuff, as their ridiculous rate of fire meant that even with 15% hit chance they were still going to get a decent DPS
In Dawn of War 2
Stormtroopers are DoW 2's equivalent of DOW's Kasrkin, they appear in all games but only become widely playable during Retribution, where the Guard becomes a playable faction. You only fight alongside them in the original DoW 2 and you get to control two squads of them on one mission during Chaos Rising. They use Hot-Shot lasguns with armor-piercing effects. Stormtroopers can be upgraded with multiple "kits" that lets them be more effective to different targets and fit certain circumstances.
The kits are:
- Assault kit, which increases their damage output and range and reload speed, but now actually costs something and makes them take more damage as well. Usually passed up in favour of melta, but still useful for dealing with some elite infantry and commanders.
- Anti-tank kit, which easily makes them the best hunter-killer unit the Imperial Guard have available in the game. Their melta guns and melta bombs allow them to wreck vehicles, fuck up enemy power supplies, and to a lesser extent, tear up enemy commanders and superheavies.
Unlike their original appearance in DoW, stormtroopers this time round actually have a role other than being guardsman squad 2.0. Their weapon options and ability to infiltrate make them ideal for removing high priority targets like enemy vehicles, elite units, or commanders. They can also be used to disrupt power supplies and decap points. Although stormtroopers are a bit tougher and have more dakka than regular guardsmen, their unit size is much smaller (compare 5 troopers to an infantry squad's maximum of 12) and they fare even worse in melee. With the addition of a sergeant and commissar, guardsman infantry squads can reinforce three troopers at a time for a fraction of the cost of a stormtrooper, which makes them a whole lot more resilient in the field when combined with a reinforcement point such as a Chimera.
On Tabletop
Stormtroopers are difficult to classify in tabletop. Many players eschew them, since the Imperial Guard can field cheaper Infiltrators with carapace armor (and better range as part of the bargain) via Veteran Squads, and Veterans can score as part of the bargain (but so can Scions in their own codex). On the other hand, Stormtroopers deep strike OR infiltrate by default, come with AP3 weapons (which means they are the bane of not only marines, but other infantry armies, such as Dark Eldar, Eldar, and especially Tyranids (as if the bugs needed even more ass kicking). However, Veterans are a heck of a lot cheaper and are generally more flexible given that they can either take carapace armour, or for even cheaper (heh heh), get stealth and those mine things that stop the enemy getting +1 attack on the charge.
TL:DR The only differences between Storm Troopers and Veterans is that Veterans can choose between 3 squad upgrades and have longer range (but no ap) and the Scions get deep strike and AP3 lasguns with a 4+ save standard.
A Stormtrooper Squad used to come with one of the following rules active (and you got to pick which for each Stormtrooper Squad) via the Special Operations rule:
- Reconnaissance: Scouts and Move Through Cover.
- Airborne Assault: Rerolls scatter dice when deep striking.
- Behind Enemy Lines: Infiltrate instead of Deep Strike, and all their weapons count as Pinning the first time the squad fires.
With the new codex, they just get deep striking and move through cover. While this is considerably less customisable awesome, it does ties in better with the new "army of faceless, identical elite soldiers who all obey orders perfectly" vibe GW pushed through with their new cdex.
Where Stormtroopers come into their own, however, is as surgical strike units. Suffice to say, Stormtroopers are amazing units when used for target elimination - nobody likes taking AP3 fire from anything(except, you know, TEQ) they also provide easy deep-striking meltas that the Imperial Guard lacks, and are a comparatively mobile and deadly force, who have average to good basic guns and lots of cheap special weapons. Stormtroopers can take an attached transport in the form of a Chimera or a Taurox Prime, to make them even more mobile after they deep strike.
They can also be taken as a stand-alone army thanks to their new Codex:Militarum Tempestus, giving an effective and killy surgical strike to any other army. Tactics and review can be found here. This codex effectively makes Inquisitoral stormtroopers viable again - it can ally with Inquisition as Battle-Brothers. That alone makes it awesome and full of win - even if it is extremely small and doesn't include anything special except dedicated orders.
A common joke amongst /tg/ is that in order to win, you must spam MOAR STORMTROOPERS.