Plague Marines
Okay, how am I going to put this: you take a Chaos Space Marine, mix it with Nurgle, voilá!; you have a Plague Marine, who is pretty much a walking sack of bile, disease, and rot, just like Nurgle would want!
Seriously, plague marines are tough bastards, not just because they're guys with power armour (even if it is heavily corroded); they're guys with power armour and bodies that have rotted to the point where they've lost their weakness of depending on vital organs for survival as they largely don't require it anymore. Thus, plague marines are incredibly tough to kill as nothing short of blowing their bodies to oblivion or bathing it in burning promethium will put them down. And if they die, that'll still make Nurgle happy, for there will be a body to rot and they will have received his glorious gift of the inevitable end (but Nurgle will be sad to see one of his children die).
Plague marines are usually armed with a bolter that is in very poor condition thanks to the fact it has been decaying for a pretty long time. Since plague marines are too busy not dying in their disease-ridden bodies, they won't begin fixing them. 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.
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.