Power Armour
Power Armour is a science fiction concept of armour which increases the strength, speed, and reflexes of those who wear it. It features heavily in science fiction/fantasy settings such as Warhammer 40,000.
Starship Troopers
Like so many military science-fiction concepts, the modern idea of powered armor dates back to the Mobile Infantry of Heinlein's Starship Troopers. The "Marauder" suit is bulky, with integrated thrusters and heavy weapons (including a "Y-rack" that lobs atomic weapons to the side of the MI). Their primary purpose is not to destroy indiscriminately (though they certainly can), but to "make war as personal as a punch on the nose" -- to drop in and destroy with precision, in order to break the enemy in exactly the right way.
Heinlein never discusses pauldrons, but the Space Marines certainly take after the Mobile Infantry's other aspects.
Space Marine Power Armour
The most iconic users of Power Armour in 40k are the Space Marines and the Chaos Space Marines. Made of ceramite which will deflect all but the most powerful of weapons, Power Armour possess many life support systems designed to keep the Space Marine inside alive. The Black Carapace, one of the Gene-Seed organs, is specially designed to interface with the Space Marine, and is the last organ implanted in Codex Chapters. Amongst its features, Power Armour possess auto-senses which enhance the Marines already considerable senses, injects pain killers in the event of lost limbs, and recycles the waste of the body into a nutrient paste which will keep the Marine going for up to fifty days without needing to eat again. The power source is a backpack mounted generator which needs initializing, but after that can take solar energy to keep itself going.
There are eight types or Marks of Power Armour used by the Astartes. Regardless of their type, they all have massive Pauldrons.
Mark I: Thunder Armour
The first type of Power Armour designed, these were used by many of the techno-barbarians of Terra. They provided the basic protection against weapons and enhancements to upper-body strength, but that is all - the suit was incapable of supporting its own weight and did not provide any protection to the legs. Since they were only used on Terra as well as a terraformed Luna and Mars, there was no need to protect them against the void. Though the lack of life support systems and much lesser degree of protection make them essentially useless in the 41st millennium, several Chapters retain sets of Thunder Armour as ceremonial pieces of armour.
Mark II: Crusade Armour
Designed by the Adeptus Mechanicus with the Great Crusade in mind, the Mark II armour was fully enclosed and contained all the life support and auxiliary systems now common among the Space Marines, like a waste recycling unit and automated medical equipment. Much of these newer additions were made possible by a more efficient cooling system, which allowed a considerable reduction in the size of the powerpack. The helmet also came with a bunch of enhanced sensory equipment but was bolted directly onto the armour, preventing the wearer from turning their head. Overall protection and flexibility was much improved, especially since the legs were now enclosed in armoured hoops and came with their own servomotors. Unlike the Mark I suit, the design is still sufficiently sound to remain in active - albeit extremely limited - use, well into the 41st millenium.
Mark III: Iron Armour
Mark III armour was first conceived during the Squat campaigns (later retconned to boarding actions) of the Great Crusade. It was pretty much a modified Mark II designed to provide better frontal protection for close quarters combat, essentially fulfilling same role that Terminator armour would later fulfil. By the time of the Horus Heresy, the Mark III was slowly being phased out and replaced by Terminator armour, but it's still fairly common among the Traitor Legions.
Mark IV: Imperial Maximus Suit
Now having access to more of the Standard Template Constructs, the Mechanicum was able to further refine the power armour's internal systems. In addition to having more advanced visual sensors, the helmet was now capable of movement. The suit was also made a whole lot lighter than before while managing to further improve on the Mark II's protective capabilities. Although the chest power cables were once again relocated to the outside of the plating, they were given some level of armoured sheathing to protect them from damage. As the Legions were either fully or partially re-equipped with these suits by the time the Horus Heresy began, Mark IV is one of the most prevalent types of armour among the Chaos Space Marines.
Mark V: Heresy Armour
In between production of the Mark IV and what would be the Mark VI, both Loyalist and Traitor Legions found that they were running out of replacement parts for damaged systems. This would result in several Legions taking parts from older Marks and inadvertently making a brand new Mark of Power Armour. Although appearances varied widely as a result of its adhoc nature, some form of standardization was achieved. One of the most notable was the introduction of molecular bonding studs on the left pauldron and both greaves, which made them look totally Metal. Probably one of the most common suits of armour in service among the Traitor Legions, since this was what most of them were wearing when they retreated to the Eye of Terror
Mark VI: Corvus Armour
The much beloved Beakie armour. Designed as a stopgap measure while newer equipment remained in development, it incorporates some of the newly developed Mark VII features into the battle-proven Mark IV design, producing a suit of armour that is in many ways equal to its descendants. Although it offered no additional protection, Mark VI armour was the first to feature a redundant power system and parts that are slightly interchangeable with those of other marks. Somehow, it also manages to be lighter and fit together more smoothly than the current Mark VII Aquila, allowing for quieter movement, while the helmet includes further improved sensor systems in its, uhm, "beak". It was named the "Corvus" pattern after Primarch Corvus Corax of the Raven Guard, as the XIX Legion was the first to be selected for field testing the armour. Due to the design's inherent stealthiness and legacy, it still remains the preferred armour among the Sons of Corax, who tend to be saddled with older equipment anyhow.
Mark VII: Aquila/Imperator Armour
The most common Mark of Power Armour among loyalist Space Marines, Mark VII armour was still being designed when the Traitor Legions reached the Sol System and seized Mars. When this fact became all too foreseeable, Rogal Dorn ordered the design teams transferred to Terra to prevent the Traitors from seizing it. Mark VII featured completely covered chest and arm cabling, a distinct helmet that provided more protection, a high level of compatibility with the previous Marks, and also bore the Imperial Aquila on the chest, which was first used there to provide quick identification of the Loyalist Marines during the chaos of the Siege of Terra.
Mark VIII: Errant Armour
Jes Goodwin originally designed it with awesome Power Fist-style hands, a modified helmet, a streamlined power pack and a more flexible leg-and-ankle joint. Games Workshop only bothered with using the altered breastplate, so the overall design looks like a regular Mark VII with a collar. Breaking the trend of reverse-compatibility between newer and older marks is the fact that the armour can only accommodate the helmet designed for it, which is probably a major reason why it has yet to be widely adopted among Space Marine chapters (that, and the Adeptus Mechanicus' head-up-own-arse tendencies when it comes to distributing cutting-edge technology). Because of its rarity, the armour is generally restricted for use by senior officers only, and even then they'll usually only be able to wear the breastplate. The Minotaurs chapter appears to be the only exception here, as almost all of their battle brothers have access to full suits of armour.
Aegis Armour
The Power Armour of the Grey Knights, Aegis Armour is master-crafted on the forges of Titan and inscribed with prayers and wards to prevent Daemons from possessing it. Based on parts from Marks VI, VII, and VIII, within the breastplate of each set is a copy of the Liber Daemonica. It frequently bears a stormbolter on its left forearm, keeping both hands of the wearer free to use. There is an Aegis/Grey Knight version of Terminator and Dreadnought armours, too.
Sisters of Battle Armour
Less bulky than the Space Marine armour, as they're worn by normal sized humans, the power armour of the Orders Militant of the Adepta Sororitas provides the same ballistic protection that Space Marine armour does, and gives them enough enhanced strength to carry bolters in combat.
Whatever the Hell Titus's Armor Is
In Warhammer 40000: Space Marine, the Marines are wearing what looks like regular Mark VII Aquila Armor. However, it appears to be far less bulky in comparison to similar armor portrayed in official artwork or Dawn of War, suggesting it might be different. For one thing, it appears to be much more streamlined, with lower pauldrons that aren't quite as fucking enormous, and with more head room and mobility in the arm sections. This becomes very apparent when using ranged weapons, like the Bolter. This streamlining was likely done to avoid hilarious amounts of clipping.