Plague Marines
Plague Marines are Chaos marines who have sworn themselves to The Plague God. In return for their loyalty; they've been blessed by Nurgle's many contagions and tasks them with spreading their gifts to the rest of the galaxy. Because the galaxy isn't too keen on having a diseased bag of liquefying flesh masquerading as a human being get within visual range; Papa Nurgle's diseases and power have bestowed them with near limitless endurance to aid in their endeavors, allowing Plague Marines to shrug off attacks that would cripple space marines like they were mere scratches. The most powerful of plague marines are called Plague Champions, who are the most horribly diseased and strongest of the bunch.
A combination of being encased in power armor (even if it is already corroded beyond reasonable use) and being bestowed the characteristics of an undead corpse makes Plague Marines incredibly tough to kill, as anything short of being blown to smithereens or being thoroughly bathed in promethium will stop them (seeing as flames purify microorganisms and turn flesh to dry ash; the marines effectively lose their advantage in the face of fire). Like all of Nurgle's servants: a Plague Marine's highest ambition is to die and rot, as that is the greatest gift Nurgle can give to his followers, although being the benevolent servants that they are; the marines are more content to share the gift of death to more "unappreciative" individuals before receiving it themselves.
Plague marines are usually armed with a bolter, although they can still use any other weapon that the traitor legions possess like heavy bolters, plasma pistols, and missile launchers. They are typically in bad condition due to lack of maintenance and the generally poisonous environment plague marines bring with them. Because corrosion and ruin is but another aspect of Nurgle, they're not keen on repairing their equipment, although despite their weapons decaying, they never seem to have any problems with them malfunctioning at all.
They can also arm themselves with a combat blade that can unleash Nurgle's Rot on it's victims. This doctrine dates back to the Horus Heresy where Mortarion equipped every member of the Death Guard with a bolter, bolt pistol, and a close combat weapon and told them to figure out for themselves what weapon to use. Another one of their custom pierces of equipment are blight grenades, which are frag grenades shaped like diseased heads (or made from an actual head taken from a plague victim, who can sometimes still be alive and aware of its fate.). The grenade's damage is two-fold; first is that its shrapnel are infected with diseases, afflicting anyone wounded by it with a myriad of lovecraftian horror plagues. The second is that it also spreads toxic spores into the air upon exploding, ensuring that even if a squad takes cover from the grenade; they still aren't safe if they inhale the poisoned air that surrounds the blast radius.
Most plague marines are in the McDonald's Legion—the Death Guard—and serve their lazy boss in his Plague World, where they drink tea and don't do all that much, thanks to the Black Library and Games Workshop shelving them in favor of the Black Legion and Iron Warriors.
On the Tabletop
On the tabletop, Plague Marines have long been one of the most used troop choice in the 4th edition Chaos Codex, possessing an extra point of toughness due to Mark of Nurgle and also having Feel No Pain, and can equip anything from the armory that normal Chaos Marines can, unlike the other cult marines. They were, for a damned long time, easily the most durable infantry unit for cost CSM had. Even better, they also had True Grit, which let them single-hand their Bolters for an extra attack. In 5th edition, however, they lost this advantage, and they finally had competition hitting the table in the form of the Rubric Marines, which whilst they lack FNP, special weapons, and the toughness bonus, came equipped with AP3 bolters and a 4++ invuln save that allows them to tank the one thing that Plague Marines can't normally handle: the likes of Battle Cannons and Earthshaker Guns. Whilst Plague Marines were still objective-holders par excellence (seeing a squad of 9 hold off 40+ Boyz for an entire game isn't unheard of), more efficient for points, and more versatile, the arrival of their Tzeentchian counterparts meant that they no longer held a complete monopoly on such a battlefield role.
6th edition gave them a mixed bag with Feel No Pain's changes, but gave them a few new goodies: they also have poisoned weapons, and since their cost hasn't changed, it's likely that they will remain a mainstay of many competitive lists. Their only drawback, besides cost, is that have lower initiative than other marines, which most players don't care about. While they got buffed by the 6th edition with the changes to Feel No Pain, the Mark of Nurgle applying to Instant Death, and the addition of poisoned attacks, buffs to the rest of the codex means they do have some good competition now.