"Reinterpretation of the final(ish) confrontation in Half-Blood Prince"
Dumbledore: You're not going to kill me, i know that in your heart you're really a good person!
Malfoy: I'm not good! I'm not! How dare you accuse me of that you bastard! I'm just a coward! I swear!
Even more spoilers!
"The Harry-as-Horcrux theory - details"
So, going in "real life" chronological order (and this is just based on my memory of events, so i may have missed something)
Voldemort is planning on killing Harry Potter because of the prophecy (i've kind of forgotten what the prophecy was, but that's not really important =)
He apparently decides that he's going to use the energy from that death to create his final Horcrux, but obviously he doesn't suceed in killing Harry.
Here we enter the lands of rampant speculation.
There's several deaths at the time, both Harry's parents and Voldemort's himself (although i'm not sure his would really count as an adequate power source.)
Version 1: Voldemort had the spell all primed and ready to go, then he gets killed, everything goes haywire, and the spell fires off on its own with Harry as the target.
Version 2: Voldemort had the spell all primed and ready to go, then he gets killed. As he's dying he says, "oh shit, i better store this last piece of sould while i still can." He either fires it off randomly and it hits Harry, or he picks Harry as the only nearby target.
So the question is, does Voldemort know that he created a Horcrux at that time, and does he know it was Harry?
So Voldemort is "dead," and Harry is now encrusted with a piece of his soul. As a result we get all the overlaps with Voldemort that are revealed throughout the series. Harry can speak parseltongue, the sorting hat thinks maybe he should be in Slytherin, Harry gets some weird psychic connection with Voldemort.
The only significant question is if this is true why does Voldemort keep trying to kill Harry? Two possible answers i can think of, either Voldemort doesn't know, or Voldemort is pissed that part of his soul ended up in Harry and knows how to get it back if he's there when Harry dies. This would account for the otherwise stupid order to his Death Eaters that none of them is to kill Harry (disregarding the horcrux theory for the moment, it's more likely that that's just because Voldemort is a pridefull fool, but back to the theory.)
So how does this get resolved?
Dark dramatic ending: Harry kills Voldemort, then finds out he has to die in order for the world to be safe.
Happily ever after ending: Harry kills Voldemort, then has to undergo some weird psychic surgery so the piece of soul can be pulled out and destroyed. (Or the same thing in the other order of course)
Ironic ending: (Almost the same as above) Voldemort captures Harry and chooses to extract the soul bit before he kills him. He succeeds in extracting the soul bit and _then_ gets whacked.
Ultra-cheesy ending: Harry kills Voldemort, but still has a piece of his soul in him. "It's okay Harry, as long as you have love and happiness and sunshine and fuzzy bunnies in your heart Voldemort's soul will be powerless and everything will be happy sunshine yay oohhh look fluffy bunnies!"
Silly alternate 1: The horcrus is actually Harry's _scar_. He needs to destroy the scar in some manner to get rid of the soul bit. Maybe get it magically healed somehow, maybe burn it off, maybe make a new scar across it (good use for that Septum spell?) Or alternately some weird spell that makes the scar hop off him and bounce about until they stab it a lot.
Silly alternate 2: They kill Voldemort and get rid of the soul through some means, and Harry finds out he isn't a wizard at all, it was just the peice of Voldemort's soul letting him use magic. Harry is sad and has to go live with the muggles. You suck Harry.
Silly alternate 3: They don't find out that Harry has a piece of Voldemort's soul, or they go with the Ultra-cheesy happy ending. Harry gets married, has kids, dies, and a few days later Zombie King Voldemort rises from the grave! Perhaps just as Harry's youngest and most beloved child is starting his or her first year at Hogwarts, and only that child can defeat the slavering corpse that has become Voldemort...