What are some examples of foreshadowing in the story?

Foreshadowing is a literary technique whereby the author drops subtle hints of what is going to happen later in the story. There are many examples of this in The Great Gatsby, but here are just a few of them:

[Gatsby] stretched out his arms towards the dark water in a curious way... I glanced seaward and distinguished nothing except a green light... that might have been the end of a dock. When I looked once more for Gatsby he had vanished, and I was alone again in the unquiet darkness.

Nick is the narrator of these events, of course. The green light can be said to symbolize Daisy, and Gatsby stretches out his arms towards the light in the hope of being with her. Yet when the green light disappears, so does Gatsby. This indicates that they will never be reconciled, an impression confirmed by another piece of foreshadowing later on:

 The day agreed upon was pouring rain.

Gatsby and Daisy agree to meet up; but on the day of their meeting it is raining. It seems that the weather reflects something about their relationship. It is not surprising that it wouldn't work out between them, especially when Daisy's feelings for Gatsby are so superficial:

"They're such beautiful shirts," she sobbed. "It makes me sad because I've never seen such—such beautiful shirts before."

Isn't Daisy so incredibly shallow? Yet this is the fullest extent of her feelings towards Gatsby. If two people in a relationship have such a different understanding of love, then there is no future between them.
Gatsby's death is foreshadowed in a number of places too:

I couldn't sleep all night; a fog-horn was groaning incessantly on the Sound, and I tossed half sick between reality and savage frightening dreams. Toward dawn I heard a taxi go up Gatsby's drive and I immediately jumped out of bed and began to dress—I felt that I had something to tell him, something to warn him about and morning would be too late.

Nick has had a terrible nightmare. What could it have been about? We don't know, but it certainly points towards an unhappy ending for Jay.

[Life] starts all over again when it gets crisp in the fall.

These are the words of Jordan Baker. Gatsby decides to take his fateful last swim in the pool on the first day of fall, a time of death and rebirth. Gatsby will die, but all the shallow, superficial rich folk of the two Eggs will start over as if nothing has happened. The fact that so few of them have the decency to attend Jay's funeral confirms this.