Originally Posted by General Abilities

Percy, as a demigod, has these abilities and traits:

ADHD: Percy's supernatural alertness and keen senses that keep him ready for, and alive, in battle. It also lets him analyze his opponents fighting style as well as pick up minor details about an opponent, such as where their muscles tense so he can tell which direction they'll attack from. This is one general trait of demigods.

Dyslexia: Percy's brain is "hard-wired" for reading divine Ancient Greek instead of mortal languages. During his time at Camp Jupiter he learned to understand, and possibly speak, Latin to an unknown degree. This, along with ADHD, is a trait common to most demigods.

Fighting Skills: Percy is a naturally talented and expert swordsman, capable of holding his own against and even defeating larger, more experienced, and more powerful opponents, including gods and Titans as well as monsters. In The Son of Neptune, even after losing the Curse of Achilles, he is still shown to be able to fend off an entire army of continually resurrecting ghosts by himself while still protecting Frank. His Greek training and unpredictable, solo fighting style make him particularly dangerous to the demigods of Camp Jupiter, who are used to fighting as a group, allowing him to easily defeat multiple opponents at once. According to Frank, Percy "fought like a demon." When possessed by eidolons, Percy fought Jason Grace on even footing (Piper couldn't believe the speed of their sword fighting) and injured him to a point that he was knocked unconscious. However, it should be noted that Jason was distracted by Piper's charmspeak at that particular moment, which allowed the possessed Percy to exploit the opening in Jason's defense.

Curse of Achilles (formerly): After bathing in the River Styx, Percy was given supernaturally superior speed and strength as well as invulnerability except for his vital spot opposite of the navel. With the Curse of Achilles, Percy's own combat skills are enhanced to the point where he can single-handedly defeat entire armies as well as gods like Hades and Titans like Hyperion (albeit he had some help in defeating Hyperion). He later loses it by touching the Tiber river as it was a Greek blessing and he could not enter Roman territory with the curse.[1][2]

Empathy Link: Percy has a psychic connection with Grover called an empathy link. In The Son of Neptune, Don the faun said that Percy had an empathy link with another faun who is Grover.

Eye of Horus Symbol: Percy has an image of the Eye of Horus drawn on his palm, which can allow him to summon Carter Kane wherever he is just by speaking his name, though Percy can use it only once. So far Percy hasn't used it yet.

Originally Posted by Demigod Abilities

As a son of Poseidon; one of the Big Three, Percy is an extremely powerful demigod. He has divine authority over his father's domains and subjects. Percy is considered to be the most powerful demigod in Camp Half-Blood. Hazel had considered Nico di Angelo the most powerful demigod she knew, until she met Percy, and believed that Percy's power rivaled Nico's and Jason's abilities. Nico later states that, even compared to the rest of the Seven Heroes of Olympus, Percy is the most powerful demigod he has ever met. Both through his father's authority and his own inherent power, Percy's abilities include:

Water-Induced Abilities: When in contact with or in the presence of water, Percy gains a disproportionate amount of superhuman clarity, strength, speed, agility, and endurance equaling a god and he has shown to be more powerful than Ares while in this state. In The Lightning Thief, Percy was able to defeat Luke in the Camp Half-Blood swordsmanship class after he'd doused himself in water. In addition, after Percy was pushed into the creek during Capture the Flag, he effortlessly defeated four children of Ares in rapid succession, including Clarisse, with ease. However, this only lasts for a limited amount of time unless he is completely submerged in water. He also heals himself from any wound and most poisons when he comes into contact with water, the amount of water and time needed for the healing being proportionate to the severity of the wound.

Hydrokinesis: With the power of the sea within him, Percy can control every form and great volumes of water, being even able to summon and heal his wounds and cure himself of most poisons with it. Percy can control water almost omnipotently. He can control it in order to make it explode, or use it to grab something. His hydrokinesis abilities include:

General Hydrokinesis: He can create water from petrified seashells, as well as being able to create water with his own energy and summoning the "force of the ocean" to his will, as long as he concentrates hard enough. He can also harden water into an almost solid shape.
Hydrogenesis: Percy can create water from his own power, though it takes much of his energy for him to do so. Percy did this while at Mount Saint Helens, creating water out of nothing to cause a volcanic eruption. He also uses this skill while creating his own personal hurricanes. While traveling on the Argo II during The Mark of Athena, he presumably used this ability while combining his powers with Jason Grace's to create powerful storms.
Healing Factor: Since he is the son of Poseidon he can heal most wounds and cure most poisons when in contact with water.
Water Propulsion: He can control the water around him to propel himself through water. Percy can shoot water, not only from being in water, but he can blast the own water he creates.
Underwater breathing: Percy can breathe underwater and diffuse the oxygen in the water to create oxygen bubbles that allow his non-hydrokinetic friends to breathe underwater. However in The Last Olympian he was unable to breathe in the River Styx.
Water Immunity: Percy can fall from great heights into water, and is unaffected by any amount of water pressure. He does not get wet if submerged in water, unless he wants to. Percy can dry items underwater (as long as he holds onto it), such as a lighter.
Water Solidification: Percy can harden water into an almost solid shape. He can use this power to walk on water, by increasing the surface tension of the water to the point where it is solid enough for him to stand on, and water constructs. So far, he has demonstrated creating a strong water shield, and on two instances in The Son of Neptune, he hardened the water into giant hands that followed and imitated the movements of his own hands.
Sailing Skills: Percy possesses an intimate awareness of any ship he is on (sailing ships, canoes, motorboats, possibly submarines); being able to telekinetically operate one (as well as anything related to the ocean) because he has perfect bearings on the ocean, he can easily navigate his way at sea.
Communication: Percy has divine authority over and can talk (normally and telepathically) to equines and sea creatures who mainly treat him with deference and lordly respect. He can also speak to other children of Poseidon underwater (seen in The Sea of Monsters, in a conversation with Tyson).
Atmokinesis: Percy can summon hurricanes and other types of storms, but the extent to which he can control them is as of yet unknown. Percy's hurricanes have been shown to be powerful enough to douse the fires on Hyperion's body, leaving the powerful Titan vulnerable to attack. By the events of The Son of Neptune he is able to sustain the storm with less effort than his first use of the skill against the Titan Hyperion, although it still drains him over time.

Electrokinesis (limited): Percy used this skill unintentionally on one occasion, while creating his own miniature hurricane to fight Hyperion. Sparks of lightning appeared as his hurricane increased in power. His control of this ability, however, is far less than that of a child of Zeus and appears to be a limited side effect of his storms.
Aerokinesis (limited): Percy can summon strong winds, which he could use to create storms such as hurricanes and typhoons.
Geokinesis: Percy can generate earthquakes and (consequently) cause volcanic eruptions, but his control of this technique is less than that of a child of Hades.

Cryokinesis: Percy can use cryokinesis to a small degree. He is able to use the ice and snow around him to make an icy hurricane, as he does during the battle in Alaska in The Son of Neptune. He can also manipulate frozen or icy water around him, demonstrated during his interrupted fight with Thalia in The Titan's Curse.

Heat Resistance: Percy has a far higher than normal resistance to heat and burns, similar to that of a Cyclops, due to his father's oceanic nature. He was able to survive being engulfed by lava thrown by the telekhines, though it began to get more painful the longer he was in contact with it, as well not being killed by the super-heated steam from the eruption of Mount Saint Helens.

Toxikinesis (limited): Percy can control and manipulate poisons, as seen when he beats Akhlys in Tartarus in The House of Hades. This is limited, though, as poison is only part water. However, this may only be possible in Tartarus, as the laws of nature act differently there. The full extent of this power is unknown although he is able to control it well enough, when angry, to the point of terrifying Annabeth who even asks him to stop. In The Blood of Olympus Percy tried to divert the poison Polybotes attacked him with, but did not due to his fear of this power.

Originally Posted by Magical Items

The Minotaur's Horn, he obtained this when he killed the Minotaur after it supposedly killed his mother, Sally Jackson.

Anaklusmos (Riptide)
Riptide
Anaklusmos (Riptide in English), made with celestial bronze, given to him by Chiron to fight monsters. When uncapped, it becomes a 3 foot tall double-edged celestial bronze sword and causes the fear of most monsters around it. Riptide is usually kept as a ballpoint pen when not in use, and will always return to Percy's pocket. It used to be the weapon of Hercules, who got it from Zoë Nightshade. In the movie, Riptide can deflect blasts from Zeus' lightning bolt. When combined with his hydrokinetic powers and Curse of Achilles, Riptide becomes an "arc of pure destruction."
The 12th Legion's Eagle, Percy seized the Eagle from the undead army of the frozen Roman Camp on the Hubbard Glacier during The Son of Neptune. He later used it during the battle at Camp Jupiter, where he used its lightning to destroy hundreds of monsters before passing it to Dakota.

Medusa's Head, Percy received it at the end of the first book. He cut it off and sent it to Olympus, but Poseidon sent it back. Percy, having no need for it left it with his mom, Sally Jackson. His mom uses the head to petrify her abusive husband Gabe and then sells the resulting "statue" as an art piece named The Poker Player.

Stygian Ice Whistle, a special dog whistle made of Stygian ice that was cooled in the River Styx. It was given to him by Quintus (Daedalus) to summon Mrs. O'Leary and shattered after it is blown once. Percy used it when his friends were having trouble fighting an army of monsters in The Battle of the Labyrinth.

Wristwatch shield, a wrist watch which turns into a shield, given to him by Tyson. It was badly dented by Dr. Thorn in The Titan's Curse. Tyson came back and fixed it in the beginning of The Battle of the Labyrinth. It was lost later in Battle of the Labyrinth when thrown at Kampê. It was inscribed with the images of the events of The Sea of Monsters, including Percy fighting the bronze bulls, Annabeth killing the Laistrygonian, Tyson riding Rainbow the hippocampus, and Tyson battling the Hydra whilst holding a box of doughnuts.

Nemean lion's pelt, obtained in The Nemean Lion Skirmish, when he planned the death of the Nemean Lion. He sacrificed it to Poseidon in The Titan's Curse.

Sand dollar, given to him for his 15th birthday by his father. He splits it in half and gave one half to the Hudson River and the other half to the East River gods to stop Kronos' forces on boats in The Last Olympian.

Chameleon Armor, he used this in a game of Capture the Flag in the short story of "The Bronze Dragon". It only works from a distance.

Hermes' multivitamins, these multivitamins make the person who ate it to be immune to nearly any attack, which was used by Annabeth during the Sea of Monsters to turn Percy back into a human after Circe turned him into a guinea pig and prevent Circe from using magic against her.

The Golden Fleece, used after Annabeth was wounded by Polyphemus, he used the Golden Fleece to heal her. Then it was used to save Thalia's tree at Camp Half Blood.

Pandora's pithos, this was given to Percy by Prometheus to open it and give up hope. Later he gave it to Hestia to look after it, because "hope survives best at the hearth."

Thermos of winds, this was used by Percy and Annabeth in the Sea of monsters to escape the Princess Andromeda and Charybdis. Given to him by Hermes.

Magical Pearls, these pearls can transport a person to the sea when smashed. Given to Percy by a Nereid.

Moonlace, a flower that grows in moonlight (given to him by Calypso). He planted it at a trough at his apartment, to remember Calypso.

Javelins, these aren't normal javelins, because they have a grappling hook, and an explosive setting. Used in chariot races at Camp Half Blood. Used first in The Sea of Monsters.

Daedalus' Wings, stolen in a skirmish in the center of the Labyrinth. Now in a trash can after being thrown away, too damaged for further use.

Winged shoes, given to Percy by Luke Castellan. In the book the wings spring out when the wearer says "Maia". Percy gave them to Grover. It was supposed to be a trap from Luke, as the shoes almost dragged Grover into the pits of Tartarus, due to Kronos dragging them in. In the film he used these to retrieve a pearl.

Travel Rose, which he used in The Sword of Hades to return to the world of the living after having returned Hades’s sword.