"It does not do to dwell on dreams and forget to live, remember that."
     -- Albus Dumbledore

While Dumbledore's statement above makes good sense, it wouldn't do Harry any harm to try to analyze his dreams a little more than he does. Often there are important clues in his dreams to what's going on. As a matter of fact, Harry's extra-sensory powers are not limited to prescience. Besides the dreams, he often senses the presense of another person even when they aren't visible to him, hidden in the dark (PA3).

Dreams
Harry made the mistake of telling Mr. Dursley about a dream he'd had about a flying motorcycle. His Uncle nearly crashed the car from hollering at him; the Dursley hated to hear about anything acting in a way it shouldn't. (SS2)

When he was younger, Harry had dreamed and dreamed of an unknown relation coming to take him away (SS2). Although at the time he had no idea, this dream would come true beyond his wildest imaginings on his eleventh birthday.

After his first trip on the Hogwarts Express, his introduction to school, and the Sorting, Harry had a strange dream. He was wearing Quirrell's turban, which spoke to him, telling him to transfer into Slytherin. The turban got heavier and heavier and tightened on his head. He saw Malfoy laughing at him, who turned into Snape, whose laugh became high and cold. He awoke after a flash of green light. The connections to Voldemort are obvious: the turban speaking to him, the high cold laugh, the green flash of light. It's interesting that Malfoy and Snape are connected to Voldemort in the dream, one transforming into the other. (SS7) This foreshadows Harry's dream in Divination class several years later, when an eagle owl flies into a chair and Voldemort is revealed there; Draco Malfoy has an eagle owl. (GF29).

After spending three nights staring at the image of his family in the Mirror of Erised, Harry began having nightmares of his parents disappearing in a flash of green light while a high voice laughed (SS13). Voldemort's voice is described as high and cold.

For several weeks after facing Voldemort for the second time in his life, this time at Hogwarts, Harry would wake up in the night in a cold sweat, worrying that the Dark Lord was coming back (CS1).

When Uncle Vernon had locked Harry in his room and barred the windows, Harry dreamed that he was on show in a zoo with a sign saying UNDERAGE WIZARD on it attached to his cage. He lay on a bed of straw being stared at by people and also by Dobby, who refused to help him, responding instead that "Harry Potter is safe!" Then the Dursleys were staring at him and rattling the bars of his cage. When he woke up, Ron was outside his window, shaking the bars to get his attention. (CS2)

After winning te Quidditch match against Ravenclaw, when Harry used a Patronus Charm to ward off what he thought were a couple of Dementors, Harry had a dream. He was walking through a forest carrying his Firebolt, following something that was silvery-white, like his Patronus. He could only catch glimpses of it and when he tried to catch up, he heard the sound of hooves. He woke up before he had a chance to dream more. The Patronus he was following was his own, which took the form of a Stag, which was also the Animagus form his father had taken. Of course, he didn't know either of these facts at this point. (PA13)

The night before the crucial Quidditch match with Slytherin, Harry dreamed first that he'd overslept and that his team had had to use Neville instead and had lost. Then he dreamed that the Slytherin team was riding dragons and that he had forgotten his broom. (PA15)

In Trelawney's Divination class, Harry fell asleep and dreamed that he was flying on the back of a huge eagle owl. He flew toward an old, ivy-covered house on a hill and entered an upstairs window. He flew on the owl along a passageway to a room which was dark because its windows were boarded up. He left the owl's back. The owl went to a chair with its back to Harry, out of sight. Harry saw two things on the floor: a large snake and Wormtail. Harry watched as someone in the chair tortured Wormtail with the Cruciatus Curse after telling him that his blunder hadn't ruined everything after all. When Harry woke from this dream, he knew it was significant and he immediately left to tell Dumbledore. (GF29)

ORDER OF THE PHOENIX DREAMS -- YET TO BE ADDED ...