A few people have asked me to do this, and I've been shamefully remiss. These are the four prophecies involving Harry that Trelawney's recited in the stories. Just for fun, I've also included the way various characters interpreted them, at the time and since.
The first prophecy (given in Chapter 11 of Saving Connor)
"The one with the power to vanquish the Dark Lord approaches… Born to those who have thrice defied him, born as the seventh month dies…He is the younger of two, and he shall have the power the Dark Lord knows not…For the elder is power, but the younger is power united with love…O guard him, O shield him, for the darkness through which he passes otherwise is vicious and hideous, and love has but a scant chance of surviving…The elder will stand at his right shoulder, loving him, but the younger will love the whole of the wizarding world…The Dark Lord will mark him as his equal, and in so doing mark his heart… The one with the power to vanquish the Dark Lord approaches, born as the seventh month dies…"
Interpretations:
By Dumbledore: Connor is the younger of two twins, born at the end of the month of July, born to parents who thrice defied the Dark Lord. His power "the Dark Lord knows not" is love. Harry, the elder of the twins, is his guardian. Without Harry, Connor's innocence and purity can be corrupted. It is necessary that Harry love Connor and Connor alone, while Connor learns to unite the wizarding world. The heart-shaped scar is the "marking as an equal" part.
By Peter (and others): Nothing in the prophecy says that both the elder and younger are born at the end of July. Thus, it can mean Harry, as long as someone who loves him stands at his right shoulder. Harry does love the whole of the wizarding world, with his instruction in Light morals and Dark traditions, and that also could be the power the Dark Lord knows not. He was not guarded, and as a result he passed through "vicious and hideous" darkness. He was marked by the Dark Lord, and that left a marking on his heart.
The second prophecy (given in Chapter 39 of Comes Out of Darkness Morn)
Five weeks before the time of longest light
There comes one who puts lesser foes to flight,
Who has a soul and magic cold as ice.
Now comes the hour
Of the black one's power,
And he shall die by the wand of the sacrifice.
Now comes the hour all truth is revealed,
Now comes the hour the gray one takes the field,
And first decision sets the path for all.
Now kindness is tested,
Now soft heart must be bested,
And on that test he will stand or fall.
Interpretations:
By Connor: At the time, the only sacrifice Connor knew was Harry, and he took "black one" to refer to Sirius, because of his last name. Therefore, he took it to mean that Harry would kill Sirius five weeks before Midsummer, the "time of longest light." (He doesn't appear to have given much thought to the second stanza).
By Harry (in retrospect): Connor's timeline was correct, but nothing else was. The "one who puts lesser foes to flight" was Voldemort, and the "black one" was both Sirius and Voldemort in his Darkness. He died by Peter's wand, which Sirius used to kill himself.
"The hour all truth is revealed"- Harry (and Connor) learned the truth of what happened on October 31st, 1981. The "gray one" was the leader of the Dementors, and this was the first species Harry freed from bondage. If he had severed their web without thinking of the consequences, as he almost did because he was sick and dizzy with exhaustion, it would have been disastrous. Instead, he followed his vates instincts, and so that (and other freeings) were successful. That was also the night that Harry had to learn to kill, something he'd been resisting doing; he slew Rodolphus with Voldemort inside his body.
The third prophecy (given in the Intermission called "Five Months" in Freedom and Not Peace)
Three on three the old one coils,
Three in its times, three in its choices,
It bears his rivals to silence and stillness,
And the wild Darkness laughs, and the Light rejoices.
Two on two the storms that are coming,
Two for the day, and two for the year,
The storm of darkness when no moon will shine,
And the storm of light that will blaze most fiercely here.
One on one all the prophecies bear down,
One is their center, and one is their heart,
And from my mouth comes no Divination again
Except those prophecies in which he has a part.
Interpretations:
By Sybill Trelawney, with Dumbledore agreeing with her: The "three on three" refers to Voldemort, making conjoined plans, because "the old one" is often used with serpentine imagery. The storms refer to two great battles he will conduct, and all prophecies Trelawney makes from now on will involve Voldemort.
By Harry and others: The "old one" refers to the old prophecy (the first one). It will come true three times: once for Dumbledore, once for Falco, once for Voldemort. "Three in its choices"- it chooses a different pair of champions to play elder and younger each time.
The storms- the storm the wild Dark brought down at Midwinter in Harry's fifth year, when, indeed, because it was a night of the new moon, no moon shone. The storm of light, on Midsummer day, was caused by the Light being pissed off at Voldemort, and was the day of the battle "here"- at Hogwarts.
Harry will feature in all prophecies Trelawney makes from now on.
The fourth prophecy (given in Chapter 1 of I Am Also Thy Brother)
At the end of all things,
Prophecies run out.
It is on humans to take wings
And makes themselves human past the doubt.
The first thing is the smallest thing,
But the center of many hearts still.
But, oh, savior, watch for the sting,
For the smallest things may kill.
The second, no one can afford
To ignore the curse that seems a wall.
But that curse is true, and from the Lord,
And its only destruction is a fall.
The third, amid the shining roses,
Waits for hearts to inevitably harden.
But there will be others' important choices
Within night's poisoned garden.
The fourth, in the old hatred curled
Has found its way to move and end.
Beware, for when you most wish to hide from the world,
You'll be taken by one who's a friend.
So much pain running without a halter,
More than is traded every day in gold.
Yet remember that even prophecies falter,
And it is up to human hands to hold
And cling together at the end of all things.
Prophecies will, inevitably, run out.
It is on humans to take up wings,
And makes themselves human past the doubt.
Interpretations:
By Harry, in retrospect: The Horcruxes will cause him a damn lot of pain to destroy, pain and spilled blood.
The ring was the first Horcrux he destroyed (not counting the diary and locket), and, physically, the smallest. Narcissa, who killed herself to destroy it, was the center of many hearts. It did indeed sting Harry with its poison, and nearly killed him.
The second Horcrux was the Sword of Gryffindor, and did require a fall to break the Curse on it- a "fall on the sword," an old term for committing suicide by stabbing oneself with one's sword. There was no other way around the curse.
The third Horcrux was the Ravenclaw wand, located in Indigena's garden. Peter's heart did harden- he intended to be the sacrifice- but Regulus's choice was what turned out to be the important one.
The fourth Horcrux will be the Cup. Harry does not know what the other parts of that stanza mean, other than having a tentative guess that the "old hatred" refers to him and Voldemort.
He has no idea what the last two verses mean, other than thinking that the prophecy approves of him letting his emotions free ("make themselves human past the doubt").