Rather like Lewis, one of her literary influences, JKR seems at least somewhat fond of allegory.

The Warlock’s Hairy Heart (the only tale in the collection not named by Ron in DH, and clearly influenced by Lewis) may be an example of allegory.

The eponymous warlock can be compared to Voldemort—both have utter contempt for emotion (which they see as weakness), and desire to be perceived in a certain way by others (the warlock sought to be admired and envied while by all appearances Riddle merely sought to be feared). Both also have a desire to remain “intact”, but end up anything but—the warlock desires to protect his heart from emotional hardship but instead destroys it; Voldemort tears his soul to ribbons to preserve his life, only to lose it. Also, both showed physical effects; the warlock's heart grew hair, symbolizing his descent toward beasthood, while Riddle's visage became deformed and steadily more inhuman with each new Horcrux.

It’s not too much of a stretch to imagine that The Tale of the Three Brothers is some form of allegory as well.

 

Most of us know the tale by now—three brothers, traveling together, encounter the personification of Death after they manage to avoid being killed crossing a river. Death—angry at having lost three new victims, but shrewd enough to see a way to rectify that—pretends to congratulate each of them, offering a reward to each of them for being smart enough to evade him.

The oldest brother, a combative man, asks for the mightiest wand ever created—a wand that will win every duel for its owner, one befitting “a wizard who had conquered Death”. So Death plucks a branch from an elder tree and fashions a wand from it, giving it to the quarrelsome, boastful brother.

The second brother, an arrogant man who is determined to demean Death further, asks for the power to summon others back from death. Picking up a stone from the ground, Death tells the brother that it holds the power to bring back the dead.

The youngest brother, the humblest and wisest of the three, does not trust Death (perhaps guessing Death's intentions), so he asks for something to allow him to leave “without being followed by Death.” Knowing he may have been outsmarted, Death hands over his own invisibility cloak.

Death then stands aside and lets them go on their way.

The brothers, with their gifts, go their separate ways, toward very different fates.

 

Beedle’s tales are presented as the wizarding equivalent of fairy tales—short stories designed both to entertain and teach some sort of lesson about life and the world. This tale seems to have one overarching lesson, as well as a few smaller ones.

The overall lesson is a rather morbid one—that certain things in this world are inevitable, and one should seek not to thwart death, but to accept it when it comes.

The first brother’s lesson is that even the greatest wand ever created cannot protect you from your own stupidity—and that, to quote the old proverb, “Pride (or rather hubris) goes before destruction.” If you have something others are likely to covet and they know you have it, they’re likely to come after it sooner or later. Dumbledore seems to have learned this lesson in regards to the Elder Wand—possibly more than a few of its holders have understood this lesson over the years, which would go a long way toward explaining why it is so difficult to track the Elder Wand’s history in-universe.

The second brother’s lesson is that you shouldn’t obsess over the past—as Dumbledore says, “It does not do to dwell on dreams, and forget to live.” Also, don’t meddle in things that ought not be meddled with.

The third brother’s lesson is that, as the Bard says, sometimes discretion really is the better part of valor (in contrast to the first brother), and that the best way to deal with something as inevitable as death is to learn to accept it, and not fear it when it comes (in contrast to the second brother). The youngest brother did not try to cheat Death (like the middle brother) or harm others with his power (like the eldest); instead, knowing he was only likely to escape Death once, he used his gift to live simply and without fear of Death, so that at the end of a long and happy life, he was able to go willingly from this world.

The three brothers can be compared to three characters we are familiar with in the Harry Potter universe—Voldemort, Snape, and Harry himself.

They already have a number of similarities—all three are half-bloods, all three were to some extent abandoned and/or abused by family, and all three found their first real home at Hogwarts.

 

The oldest brother’s role is taken by Tom Marvolo Riddle, known to the wizarding world at large as Voldemort. He definitely fits the profile—he is the oldest of the three; definitely a combative man, carving a bloody swath through the wizarding world rather like the wand he ended up coveting; and sought to be “a wizard who had conquered death” through the use of his Horcruxes. His quest for absolute power suits the first brother’s mindset.

Voldemort’s goal of power over death—of invincibility—can be traced back to numerous factors. He hated his father for leaving his mother (and, it seems, taking her will to live with him), his mother for being unwilling to at least live for his sake (his belief, up until Dumbledore told him otherwise, seemed to be that a wizard should be above something as mundane as death), his grandfather and uncle for their treatment of his mother (note that he shares names with his father and maternal grandfather, both of whom he came to hate—this definitely motivated his change of name), the other kids and most if not all at the adults for refusing to recognize that he was special (much like the Dursleys, they seem to have thought him freakish and possibly demonic—and with good reason; Little!Riddle has a definite Damien vibe going on there), and anything that would mean he was not special and unique. He seemed to seek control over everything as a result of him feeling helpless and powerless during the formative years of his life.

He seeks to become superhuman, to thwart death itself. But—much like the hairy-hearted warlock—he becomes inhuman instead. His physical appearance soon reflects his warped mindset.

Like the first brother, the Elder Wand—his prize for thwarting death—coupled with his own hubris, is ultimately his undoing.

 

The middle brother’s role is taken by Severus Snape. The central element of Snape’s character—one could argue—is that he seems to take everything personally. This fits the description of the second brother, who is seen as “arrogant.” It would have done well for someone to remind Snape “it’s not always about you, you know” every now and again.

To Snape, an attack on anything or anyone he associates with may be considered an attack on him personally. James’ derisive attitude towards Slytherin House is interpreted by Snape as an attack on him personally (to be fair, Snape’s opinion of Gryffindors is interpreted similarly by James, though James merely states that he’d rather leave Hogwarts than be in Slytherin while Snape pretty much openly calls James an idiot)—this is probably because Eileen Prince Snape instilled her son with her own beliefs on pureblood/magical superiority and the idea that Slytherin House is superior to all other Hogwarts houses.

James grows out of his arrogance. Snape doesn’t. And it doesn’t help that Snape doesn't really develop a brain-to-mouth filter until he totally screws things up with Lily.

In addition, Snape’s frankly disturbing obsession over Lily Evans—he puts her on a pedestal, despite his apparent disdain for or outright hatred of Muggleborns, non-purebloods, and non-Slytherins, which fits him right in with Mulciber and the other future Death Eaters—liken him to the second brother’s central desire, to bring the woman he loved back from death.

Snape, as I have noted before, pretty much wanted to have his cake and eat it too as far as Lily was concerned—he figured he could balance keeping a Muggleborn, Gryffindor friend (his trying to get James and James’ friends expelled could almost be considered removing any romantic competition, even if he wasn’t embroiled in a very personal conflict with them) with his love of Dark magic and association with future Death Eaters, without any consequences.

But said consequences bit him in the ass. Big time. He had the opportunity to either have Lily or the Death Eaters. He chose the latter, then spent the rest of his life pissed off because he couldn’t have both.

His frankly unhealthy obsession with Lily continued even after she was married (I have sometimes wondered if Snape didn’t think that James’ pursuit of Lily wasn’t just another way to attack him), to the point where he didn’t seem to mind letting Lily’s husband and infant son die as long as he could comfort the grieving widow. He even told Voldemort he wanted Lily, and had been led to believe he could have her as a reward for services rendered—meaning he was perfectly fine with Voldemort murdering James and Harry. It’s only when Dumbledore calls Snape on this that he says “fine, protect them all”.

After James and Lily are murdered, Snape spends the rest of his life taking his issues out on just about everybody—this brings us to another central element of Snape’s personality that he arguably shares with the second brother; his utter refusal to let go of the past.

Snape takes his issues out on defenseless kids, at least two of whom have committed no crime against Snape except to be born to the wrong parents. We all know that Snape’s treatment of Harry is based on the fact that if he had never been born, Lily would still be alive for Snape to stalk. It could be argued that Snape’s treatment of Neville (he threatened to poison the poor kid’s pet in front of the entire class, folks—and then castigate him for making a defective poison while Neville watched his poor pet die) is based in Snape’s anger that the Longbottoms didn’t die in Lily’s the Potters’ place. Even the other Gryffindors seem to have committed no real crime against Snape other than being sorted into that house (before you mention the Weasley twins, remember, they're equal-opportunity prank artists; they hit their fellow Gryffindors as hard as Slytherin).

Snape’s refusal to let go of the past—his insistence on holding on to old grudges, his refusal to forgive those who dared to oppose him—hampers him for the rest of his life. He only seems to regret things when they hurt him personally. In the end, he’s arguably more culpable than Voldemort, who has never known or sought love.

And in the end, his obsession is his undoing. Had he been able to let go of his hatred of James Potter and his love of Dark magic, he might have found friendship from Sirius and Remus—they missed Lily, too, after all. Snape might even have realized that in Harry he would have found not a carbon-copy of the man he hated but something of a kindred spirit.

Had he decided to do what was right rather than what was easy—it’s easy to hold on to hatred, while learning to move on is hard work—he might never have become a Death Eater at all.

But no. Not only did he display eagerness to subject both Sirius and Remus to the Dementor’s Kiss—despite his having been close enough to have heard the truth about who had really betrayed James and Lily—he seems to have seen Harry as a tool, object, a weapon to be protected from Voldemort and the Death Eaters rather than a human being. As I’ve noted before, Snape’s view of Harry can be compared readily with that of the Dursleys.

And so he died, alone and friendless, his last desire to look into Lily’s eyes—refusing to see the good qualities of the man behind them.

 

This brings us to the youngest brother, whose role is taken by Harry Potter.

Harry fits the profile—he is the youngest of the three, and also the humblest and wisest. Harry rejects the temptation of power (I can’t help thinking that the Sorting Hat puts the “you could be great, you know” bait forward on a regular basis), and is willing to let go of his own prejudices and hatreds (he forgives Sirius after hearing the truth, seems to feel sorry for Wormtail, befriends Kreacher, tries to save Voldemort in the end, and names his youngest son after the man he once hated more than Voldemort).

Harry is embarrassed by his fame, and would give up every last Knut in his vault in a heartbeat for a day of what Ron takes for granted—family. He learns from his mistakes—which is arguably the best indication of a wise person.

Harry understands that mastery of death is not control over it, but acceptance of it. He rejects the power of the Wand and the temptation to use the Stone for his own selfish reasons. While Snape would have brought back Lily at any costs (though to be fair even Dumbledore screwed up along those lines), Harry only used it to bring back his loved ones long enough to say "I'll see you soon--I need your support." He learned his lesson about letting go all the way back in PS with the Mirror of Erised, and the lesson was cemented with Snape's pensieve.

Unlike Snape and Voldemort, Harry—knowing that, as many times as he’s escaped death before, it may not happen again—shows every sign that he will live to a great age, pass the Cloak on to one of his children, and greet death “gladly”, choosing to leave this life with him “as equals”.

But that's my opinion. I could be wrong. What do you think?

(edited to clarify position on Harry and the Resurrection Stone)

(edited to correct minor point about Snape's brain-to-mouth filter)

(edited to correct another good point about Snape)