Prophecy

Prophetic Powers

The Oracle

Aladdin's helper (6.01 open) tells Emma that she "has been called an oracle," which seems like a very roundabout way of saying the thing. She helps Emma see more of her vision, which includes Emma's own death (6.01), and is helping Jasmine look for Aladdin (6.04). 
 
Rumplestiltskin

In his introductory scene, he sees the future from his jail cell in exchange for the baby's name (which he will need to identify her later), so that ability of his is not affected by his imprisonment (1.01). Both Rumplestiltskin and Henry say "the final battle will begin" with Emma's arrival. That could mean the S1 battle with Regina, or something that will emerge later.

In S2 we learn where he got this ability. The Seer appears as a child who has eyes in her palms but not her head. In his first encounter with her, she knows details of his past and tells him the following:

• "[Milah]'s already with child. Your wife will bear you a son, but your actions on the battlefield tomorrow will leave him fatherless."
• "Someday you'll help me again."
• "When you see the army ride cows into battle, you will know I speak the truth."

All of these things come to pass; "cows" turns out to be army slang, Rumple helps the Seer by relieving her of the burden of her power, and his self-wounding to get out of fighting leads him to become the Dark One and so to Baelfire's loss.

In their next encounter, the Seer tells him that this search for Bae will take years and require “a curse powerful enough to rip everyone from this land. You will not cast the curse, someone else will. And you will not break the curse, someone else will.” He takes her ability to see the future (whoosh, and a great deal of white light). As thanks, she tells him, “You will be reunited with your son, and it will come in a most unexpected way. A young boy will lead you to him, but beware Rumplestiltskin, but beware, for that boy is more than he appears. He will lead you to what you seek, but there will be a price. The boy will be your undoing" (2.14). She then dies.

Henry did lead Rumple to Neal, but since Rumple did not stay dead, one could claim that the prophecy has not been fulfilled.

The seer also tells him that he will learn "to separate what can be from what will be" (2.14). Rumple later tells Henry, "The future is like a puzzle with missing pieces, difficult to read and never what you think" (2.14).

Outside of this prime plot mover, a few other prophetic references occur.

• "A vision told me about you. Told me this day would come. But it didn't tell me everything. Didn't tell me what I really wanted to know. Did you ever love me." (Rumple, 2.16, while Cora advances to kill him).
• One of Pan's Lost Boys has a drawing of Henry when they encounter Hook, though it will be many years before Henry is born (2.22). The Darling brothers are in line to adopt Henry (3.09), so Pan already had figured out who he is at that point, but then Regina took him back to Storybrooke, which was inaccessible until the curse broke.
• "Now there's a hole in your heart. And someday, you'll come to me to fill it" (Rumple to Regina, 3.09).

After S3 it seems that either Rumple either no longer has this ability or no longer uses it -- it has been theorized that since he was bodily reconstituted from the Dark Vault, his acquired magic from the Seer was not part of the resurrection. Alternately, he may simply have learned better than to rely on it.

Zelena

Outside of the Enchanted Forest, Glinda keeps the Book of Records, which "chronicles the past, present, and future of Oz." "The book foretells of a powerful sorceress who will join our sisterhood as a protector of Oz. The book says that this sorceress from the west will come to this land by cyclone." Glinda thinks that this is Zelena.

Zelena later reads more in the book: "This sorceress from another land will make Oz her home until she fulfills her destiny and unseats the greatest evil the realm has ever seen." She thinks that the newly-arrived Dorothy must be the prophesied one, and herself the greatest evil.

Merlin/The Sorcerer

The Snow Queen's interest in Emma appears to be rooted in this prophecy, which was given to her by the Apprentice before he sent her to Earth. is written on a scroll found among her mementos of her time as Emma's foster mother:

I have traveled the world near and far.
My search knows no bounds.
My obsession will not leave me.
My search will continue to the ends of the earth.
One thing I know for sure,
the name of the savior is Emma.
The savior shall be my sister.
The family must be complete.

One of Merlin’s prophecies leads Arthur to Excalibur, and also to where Emma and the rest of the Storybrooke visitors have appeared (5.01). This prophecy says that the Savior will free Merlin (5.02) from his imprisonment in the tree.

More is learned about the prophecies in 5.04; despite being a tree, Merlin has communicated Arthur’s destiny as king of Camelot, that he will pull the sword from the stone. He is able to communicate with Emma while she’s a child in our world (5.01). He says that he can see “bits and pieces” of the future (5.06). This ability does not work with Nimue (5.07). It later appears that he can see multiple potential paths (5.10), not a single clear future; this may explain his subtle attempts at influence over the centuries.

Merlin’s history with the Dark One connects him to the existence of a pocket universe in the Vault. This is the same location Snow “visited” when she touched the unicorn’s horn and had a vision of Emma crushing her heart.

The Apprentice

Not sure if this should go here, or not, but the Apprentice works a spell on Lily and Emma that follows:

Let the darkness find its way from tender womb to darkest tomb/ and if it sees the light of day on distant shore where shadows loom/then let no magic give it form /and work no curse nor magic worse/ on innocents of mortals born. 

Emma Swan?

After the arrival of the airship from the Land of Untold Stories, Emma begins having visions of her own death at the hands of a cloaked figure (6.01). This is the second time Emma has exhibited some kind of foreknowledge (see her dream in 5b), although the accuracy of this vision and the motives of the Oracle are not clear. 

Unicorn Horn

When Snow and Charming touch a unicorn’s horn in S4, they each experience a vision. Charming’s is harmless, of Emma as a baby. Snow’s shows her a jungle landscape which is later revealed to be part of the Vault of the Dark One; in this vision, Emma crushes Snow’s heart.

Destiny

Rumplestiltskin often claims to believe in destiny. It's not clear whether that's a personal belief or an actual operating parameter in the show's universe, though it may explain some things about Rumple. It seems to run in the family:

"Maybe it was fate... he used to tell me that there are no coincidences. Everything that happens, happens by design, there's nothing we can do about it. Forces greater than us conspire to make it happen" (Neal, 2.14).

"Not coincidence; fate. And apparently, fate has a sense of humor" (Rumple to Regina on his selection of Henry for her to adopt, 2.19).

"Do you think it's a coincidence that the spawn of the Dark One met your mother?" (Pan, 3.03).

In addition, when Baelfire arrives in Neverland, Hook says, "It can't be chance that brought him here; Providence must be at work" (2.22).

The idea that Fate is an objectively existing force in the world is given heavy support in late S4 when we find that Emma’s old friend Lily is none other than Malficent’s daughter; they appeared to be drawn together even before the Apprentice told Lily about her origins.

Merlin finding the Grail in the desert strongly hints at other forces at work in the world (5.07).

Prophetic Dreams

1.21 Regina dreams of a mob of Storybrookers coming to kill her. Bound to a tree, "Don't let them do this to me," she begs Henry. "You did this to yourself," he answers before Emma swings the sword to (presumably) behead her.

2.04 Belle dreams of a violent confrontation between Rumple and the dwarves in the shop, at the end of which he takes on his Enchanted Forest appearance. "Stop. This isn't you anymore," she pleads with him. "Oh, it's me, dearie. Always has been, always will be." She wakes and goes to find him working magic.

2.19 Rumple dreams about a birthday party in the shop. He offers Henry his choice of objects; Henry selects a wand. Rumple uses it to turn him into a statue, which he smashes.

3.14 Right before Snow tells him she's pregnant again, Charming dreams of Emma in the Enchanted Forest, the life she would have had there, and his own fear of failing as a father.

4.06 Belle dreams of events just before her mother's death, but she has repressed the memory of her last moments. Her father later tells her that her mother died buying time for Belle to escape from the ogres.

4.15 Regina dreams that she and Robin are threatened by the Evil Queen.

5.17 Emma has a dream while in the Underworld, of a cyclone arriving at the cemetery and a monster attacking Snow. This turns out to be accurate, although the “monster” is Ruby. 

Random Bits of Foreshadowing

Hook tells Felix, "Remember what I did to Rufio? It's a far worse fate for you." Felix has his heart ripped out by Pan.

More potentially magic-laden given the source, "Your father will always be your burden, Rumplestiltskin" (Spinster, 3.08)