Poseidon was the Greek god of the sea, and also of earthquakes and horses. Mythology depicts him as being a temperamental god, who often plagued those who angered him with storms and shipwrecks. His precise powers and weaknesses depend on the particular story in which he appears, but like the other Greek gods, very little can harm him. His only real weaknesses lie in being tricked or deceived, and woe to the trickster if Poseidon ever learns that he's been duped.
As the god of the sea, Poseidon has power over all forms of water, as well as the creatures of the sea such as fish and dolphins. One myth tells of a contest held between Poseidon and Athena to determine who would be the patron of the Greek capital city. Poseidon struck the ground with his trident and caused a spring to well up from the rocks instantly. The spring was salt, however, and the olive tree that Athena planted was deemed much more useful. The city of Athens still bears her name today.
Power to Create Storms and Earthquakes
Poseidon was considered a destructive god, and many of his powers reflect an apocalyptic bent. He could call up storms and typhoons out of blue skies, drive ships into rocks with terrible waves and create new land formations by unleashing great earthquakes. When he lost the contest with Athena, he flooded the Attic Plain as punishment, and the Greek King Odysseus spent 10 years traveling across the sea outrunning the storms and typhoons that Poseidon sent his way.
Power Over Horses
In addition to oceans and earthquakes, Poseidon was the god of horses and held influence over all things equine. He rode across the sea on a golden chariot drawn by hippocampi, also known as aquatic horses, and myths tell of him fathering numerous magical horses. He seduced the goddess Demeter while disguised as a horse, and their child, Arion, was a talking horse. He also seduced Medusa when she was a human woman, and when Perseus cut off the Medusa's head, the winged horse Pegasus sprang from the blood.
Limited Sphere of Influence
As a god, Poseidon possessed very few tangible weaknesses. The most prominent was his comparatively limited influence. He had no power over the air or land besides being able to cause earthquakes, and if he intruded into those realms, it would draw the ire of whatever other god held sway there. The best way to protect oneself from his wrath was simply to stay away from the ocean.
Like all Greek gods, Poseidon was petty, given to fits of temper and capricious whims, which left no room for the opinions of others. While it made for quite a pinch if you were his target, it also meant that he could be distracted fairly easily. At times during "The Odyssey," Poseidon seems to forget about Odysseus, allowing him to make progress on his trip home before returning to torment him yet again.