Well, shit.
After thinking about it a bit, I've decided that of the five major bodies that just got dropped:
1. Quentyn Martell is as dead as a proverbial doornail.
2. Ser Gregor Clegane, the Mountain that Rides, is almost certainly dead, but that isn't the handicap it used to be in the olden days.
3. I'm leaning 60/40 that Stannis is dead and gone.
4. Jon Snow may or may not be dead, but he's almost certainly coming back and/or sticking around regardless.
5. Keven Lannister is dead as a doornail.
First, there's some pretty regular storytelling patterns in how GRRM kills off important people:
1. Nobody's dead until their death has been explicitly confirmed on-camera.
For instance: Ned got his head chopped off on-camera, and we later saw his head on a pike and his bones in a box. Ned Stark is as dead as they get. Likewise, we saw Lysa Arryn fall out the Moon Door and go splat, we saw Robb cut down on-camera and later got confirmation from dozens of independent witnesses that he died and they mutilated the body, and we saw Viserys get his crown.
On the flip side, most of the major fake-outs have been implied-but-not-demonstrated. The onion knight, for instance, was reported dead second-hand by someone who'd seen "his" head on a spike from a distance.
Quentyn Martell died on camera. Ser Gregor died off-camera, but we saw his skull in a box after hearing about an off-camera death from people who had no known reason to lie (a bit of wiggle-room, but relatively solid). Stannis "died" off-camera, and we heard about it from a single unreliable source. And Lord Snow didn't explicitly die: he took three serious but not-necessarily fatal knife wounds, collapsed, and lost consciousness. Kevin died on camera pretty explicitly.
This pattern is the main reason I'm suspicious of the Hound's apparent death, too.
2. Deaths in the middle of a chapter are real. Apparent deaths at the end of a chapter are fake-outs. Especially for perspective characters.
Countless times, GRRM has ended chapters by having the perspective character appear to die or be about to die in a cliffhangerish way, only to show us fifty pages later that they were just wounded or knocked-out or otherwise reveal the ending of their previous chapter to be a fake-out.
Ned died in the middle of an Arya chapter. Robb died in the middle of a Catelyn chapter. Cat died at the end of her own chapter, but she got better. Theon "died" at the end of one of his own chapters, but was revealed to have just been knocked out and taken captive. Tywin died in the middle of a Tyrion chapter.
There is a consistent exception, though: prologue and epilogue chapters end with the one-off perspective character dying at the end of the chapter, and as far as we know, all of those deaths have been real. But that's a special case, since GRRM establishes different narrative patterns for prologues and epilogues than for standard chapters.
Quentyn (assuming he stays dead) is almost, but not quite, a counterexample to this pattern: he got a face full of dragon fire at the end of his last chapter, but didn't actually die until the middle of the next chapter (from the perspective of Ser Barristan).
Gregor was never a perspective character, he took his mortal wound mid-chapter, and we got news of his death mid-chapter.
Stannis was never a perspective character, he died off-camera, and we got news of his death mid-chapter.
Jon Snow is a core perspective character, but he "died" at the very end of one of his own chapters.
Ser Keven died at the end of his chapter, but it was an epilogue chapter, which seems to work by different rules. By the prologue/epilogue rules, he's dead and gone.
3. Story logic
GRRM is a harsh god, but he's not gratuitously cruel. He drops bodies for a reason. Ned died to provoke the North to war, and to take his secrets to the grave. The Red Wedding was a classic tragic-hero-downfall for Robb, who both had earned his downfall and had reached a point where keeping him alive was obstructing other key story arcs: the anti-Lannisters were fragmented and needed extreme adversity to come back together; the story meant for Asha's faction and the survivors of Robb's faction to come together with Stannis's faction, which can't happen so long as Stannis and Robb both wear crowns, and neither of them had it in himself to step aside for the other.
Quentyn never had much of a role in the story. He's not needed to serve as a bridge between Danerys and Dorne (either her nephew can serve in that role, or she can just show up with a dragon and a crown and they'll figure it out eventually), he's standing in the way of both Prince Aegon and Victarion Greyjoy as suitors to Danerys (who can only have two husbands at the end of the story), and his death helped refined the rules for dragon handling, proving that a drop of Targaryen blood is not sufficient.
Ser Gregor was a peripheral and expendable character as well. Killing him off cost nothing, but helped muddy the waters for Dorne's plot, and offed the key witness who could have confirmed or denied Prince Aegon's identity (Gregor being the guy who apparently killed the real Aegon) without eliminating all avenues for eventual confirmation.
Westros isn't big enough for both Stannis and Daenerys, so Stannis has to go sooner or later. Killing him off here and now keeps the Boltons around as a boogieman (never waste a good villain) and opens the door for an alliance between the Wildlings and the Ironborn against the Boltons (Wildings under Jon Snow or Mance Rayder, Ironborn under Asha with Theon as her figurehead), which keeps the political picture nice and messy while still leaving a door open for eventual resolution.
Jon Snow's death serves a purpose, too. By the end of the book, he had become de facto King Beyond the Wall: all the influential wildlings who'd passed the wall by his leave owed him their lives and the lives of their followers, needed his leadership and support to hold the combined forces at the wall together and knew it, had sworn oaths to him, and had significant (if grudging) personal respect for him and looked to him for guidances. When the Bastard of Bolton send his nastygram to Jon, Lord Snow announced that he was leaving to answer the challenge, and just about all of the wildling warriors were set to follow him. But Jon's death at the hands of Men of the Watch breaks the ties holding the wildlings to the watch, and will likely inflame the wildlings to revenge. It's even money whether they'll respond by murderizing the watch or just picking up and heading to Winterfell to rescue their other king (Mance).
On the flipside, though, Jon Snow's story arc has some major shoes that haven't dropped. He's Robb's nominated heir as King of the North, and no hay has been made of that. He's been painted as the great man who will unite the wildlings to the realm of men to hold back the Others, which can't happen if he's dead. It's been strongly implied that he's the son of Rhaegar Targaryen and Lyanna Stark, making him the third Targaryen heir, which both fits with prophecy ("The dragon has three heads": Danerys, Aegon, and Jon) and sets up for shit to get real when his identity is discovered. If Jon stays dead, all of this setup is wasted.
My money on this count is that Jon is dead enough to break the link between the Wildlings and the Watch, but he'll get better enough to fulfill the rest of his apparent story arc.
And Ser Keven's death serves exactly the same purpose for GRRM as it serves for Varys: Ser Keven has the strength, the skill, and the political clout to rule effectively, and if he stays alive, he will hold together the realm for Tommen, which just won't do.
Now, we move on to story-internal reasons.
Quentyn got roasted alive with dragonflame and had third- and fourth-degree burns over most of his body. ASoIaF has better medicine than real-world medieval Europe, but Quentyn's wounds as described would be invariably fatal today.
Gregor was poisoned with a venom that we've been repeatedly told by reliable sources is invariably fatal and incurable at a fraction of the dose he took, and he got excellent medical treatment which we were reliably informed wasn't working in the slightest. Then his head got cut off, which usually does the trick. Sure, "Ser Robert Strong" matches Gregor's descriptions, and the timing is suspicious, but Ser Robert's behavior and his emergence at the hands of Lord Qyburn both point to him being a Wight or a Flesh Gollum or otherwise a thing created by Lord Qyburn from Ser Gregor's corpse. Especially the part about how Ser Robert never talks, eats, drinks, answers calls of nature, or removes his armor or even lifts his helmet.
Stannis's army was caught by winter, without shelter, and with inadequite supplies and cold-weather gear. They were already turning to cannibalism. And they're right next to an enemy with better supplies, a larger force, and a fortification that also serves as shelter. By any reasonable military logic, Stannis is toast. His only chance of personal survival would be to ditch the bulk of his army and abscond back to the Wall with the bulk of the supplies, and that's just not how Stannis rolls.
Ser Keven got shot in the chest with a crossbow, then stabbed a bunch of times, under the close observation of someone with plenty of time and motivation to stay and makes sure he's dead.
Jon Snow is a particularly complex case. There's several ways for him to live through this:
He may only be mostly dead. A glancing slash wound on the throat, a stab in the stomach, a stab in the back, and he passed out from shock. Assuming prompt care to stop the bleeding and treat infection, his wounds are survivable if he doesn't take more injury. There was a giant who liked him and was also being attacked by Jon's assailants standing right next to him, so the giant could plausible have held off Jon's attackers long enough for help to arrive. And it's been established that 1) Maesters have at least basic knowledge of sanitatizing wounds and even primitive antibiotics (poultices of bread mold (penicillin) are mentioned repeatedly through the books), and 2) Mellisandre is close at hand, we saw in Victrion's chapters that Red Priests can magically heal infected wounds, and Mel seems to want Jon to live.
Which segues neatly into the next point: if Jon is dead, he died with a Red Priest who wants him alive close at hand. Necromantic resurrection is well-established in the series, often at the hands of the Red Priests.
And then there's the prologue of this very book, where we get explicit confirmation that: 1) a powerful Warg can hijack a human, 2) if a Warg's original human body dies, his soul lives on in his animal, and 3) Jon is a very, very powerful Warg, although he's untrained and unpracticed. Jon could jump to anyone in close proximity, or he could jump into Ghost.
Plus, death isn't the handicap it used to be in the olden days. We've seen at least one intelligent undead being: Coldhands, a dead man of the Night Watch who seems to still be seeing to his duties. If Jon's body isn't burnt or resurrected promptly, he'll likely come back as a wight, and may come back as an intelligent wight like Coldhands. In particular the closing line of "He never felt the fourth dagger, just cold" sounds like he might be feeling himself becoming a wight. Or it might just be shock symptoms.
Come to think of it, the Warg and the Wight theory combine neatly. Regular wights are little more than zombies, whereas Coldhands, who matches the physical description of a Wight, nevertheless acts and talks like a living man. He's roughly what I'd expect if a Warg were piloting a Wight's body. Perhaps Jon's body dies can becomes a Wight, Jon wargs into his wolf, then wargs back into his Wight body at some later point.
Then there's some very specific imagery around Jon's apparent death: he looks up and sees a knight with a star emblem, covered in blood; he sees "smoke" from his stomach wound; he sees Marsh crying as he stabs Jon; and his vision fades to black as he passes out.
Remember the words of the prophecy that Mel believes refers to Stannis and everyone else believes refers to Daenerys: "When the red star bleeds [bloody star emblem] and the darkness gathers [Jon blacks out, and he's attacked in a dark corridor], Azor Ahai shall be born again [resurrected] amidst smoke [from his belly wound] and salt [Marsh's tears] to wake dragons out of stone [the blood of a King is the price for raising a dragon, and Jon is nominated heir and either cousin or half-brother to Robb Stark, last King of the North, he's probably a Targaryen prince, and he's de facto King of the Wildlings]."
Also remember Mel's visions in the flames when she tried to scry Jon's future: daggers in the dark (yup), and a shape that's a man, then a wolf, then man again. Consistent with the theory that Jon dies, his soul goes into his direwolf, then he later regains human form somehow (his original body is raised, or he wargs into another human body, or he becomes a second Coldhands as speculated a few paragraphs back).
And then there's the idea of indicative names for the Stark Direwolves:
Grey Wind was seen by Robb's allies and enemies a practically an elemental force, running fast and deadly at Robb's side.
Lady was sweet, beautiful, trusting, and fairly helpless, just like the Ladies of the stories Sansa adores.
Nymeria was named after a half-legendary warrior-princess who raised an army in the wilderness. The wolf is the leader of the vicious pack of the Trident, and is something of a legendary monster herself
Summer sounds like it's likely to be indicative of a roll he will play when the Winter ends. We'll be waiting a while for the other shoe to drop.
Shaggydog is still an absurd name. I award Rickon no points and refuse to speculate on how this may prove to be indicative.
And Ghost: the spirit of someone who dies suddenly or violently, but who will not or cannot pass along to the afterlife. I wonder what that could possibly be indicative of.