I'm pretty sure that Harry is a Horcrux or its equivalent, whether that happened intentionally or not. He does share part of Voldemort's soul. If you need confirmation of that, try Dumbledore's 'in essence divided' - methinks that's permanently cleared up. And maybe that's when Dumbledore got the inkling of what was going on.
But I highly doubt that Voldemort meant to put it there. Remember, Voldemort had learned that Harry was his bane (or so he thought, anyway), and was terrified of taking any risks. And by making Harry a Horcrux, he'd make it impossible for Voldemort to kill Harry, his biggest threat, without losing a little of himself - not just a little, but the equivalent of what he himself had. 'Mark him as his equal' - precisely, as everyone's been saying. And Voldemort doesn't take those sorts of risks.
EDIT! Due to the lovely phoenixsong, I can elaborate.
If Voldemort's got part of his soul in Harry, it's entirely due to the failed AK. With all proper worship directed at the lovely phoenixsong -
A new thought on the tearing of souls and horcruxes: Perhaps, under normal circumstances, people do repair their souls after they've murdered, which is why they don't become empty shells after a few murders. BUT, perhaps putting one's torn soul-piece in a horcrux means that the soul cannot be repaired?
So - AK is what split his soul. When the spell backfired, he lost control of one half; it fused with Harry. So he never would have had to intended it at all.
Anyway. If a person has someone's soul, or part of it, inside of them, and they're taking on that person's characteristics, that means they're using the soul - it's forming part of their identity. I think that suggests a partial fusion of souls... which would make it doubly difficult to kill Voldemort without killing Harry, because there'd be no way to separate the souls.
And can you choose which section of your soul you siphon off into a Horcrux? If you can't, and the amount of Voldemort's soul in all the Horcruxes are equal, all of them must have been made at the same time. If he didn't, then the most likely scenario is that your soul is halved each time, drawn down the middle, and there's no way you can control what's going where. But that means there are some Horcruxes that are much more important to him than others - and those are likely to be better hidden and with more dangerous protections. And if all of them threaten injury or death, and Ron and Hermione are the only ones (thus far) coming with him...
What happens if Voldemort loses his bit of soul? Can he retrieve another one from a Horcrux? Could he hypothetically take them and reassemble the bits he has left? Or is the bit of soul in him invincible as long as there's another bit somewhere else?
In that context, what happened on the night he died? Assume for a minute that it's not the last option. Did the bit of soul he used to survive come from another Horcrux? Then there's one fewer than Dumbledore thought, and Harry's doomed to a bit of a wild goose chase.