Like tpisano said, Homeric Heroes do not usually change over time. They remain steadfastly strong, courageous, determined, and skilled. While Odysseus does consistently demonstrates these traits, his journey causes him to become different in many ways.
At the beginning of the journey (not of the epic, because the epic begins in media res), Odysseus is characterized by his arrogance. He exhibits extreme hubris, meaning that his pride causes him to overestimate his own abilities. Because he is the most clever man on the Greek expedition, and because he is the one who comes up with the winning plan (the Trojan Horse), he believes that his intelligence is infallible.
After the war, Odysseus and his men encounter several setbacks, but the biggest one comes when they land on the island of the Cyclopses (one-eyed giants). They enter a cave to find lots of provisions and food, which they begin to take. However, it turns out that this cave is the home of the Cyclops Polyphemus. He returns to the cave with his flock of sheep and captures Odysseus and his men by blocking the entrance of the cave with a boulder. Even though Odysseus tries to appeal to the laws of hospitality (which are extremely important to the Greeks and considered a cornerstone of civilization), Polyphemus ignores this and eats two of the men. They are trapped, and Polyphemus continually eats two men at a time for the next few days. Finally, Odysseus comes up with one of his usual clever plans.
He gives Polyphemus some strong and undiluted wine (another indication of Polyphemus' uncivilized side, because civilized Greeks only drank watered-down wine). Polyphemus becomes extremely drunk. He asks Odysseus what his name is, and Odysseus replies, "My name is No One." (In some translations, "No Man" or "Nobody"). Polyphemus, satisfied, tells him that he will eat "No One" last because of the wine gift. When he falls into a drunken sleep, Odysseus takes a wooden stake, heats it in the fire, and drives it into the Cyclops's eye. Polyphemus screams out to his fellow Cyclopses for help, saying: "No One is hurting me!" This, obviously, causes the other Cyclopses to ignore Polyphemus. Meanwhile, Odysseus tells his men to tie themselves to the belly of the sheep. In the morning, the blind Polyphemus leads the sheep out to graze, feeling the tops of the animals to make sure the men are not escaping. Odysseus and his men escape the cave from under the sheep, and reach their ships.
At this point, Odysseus is feeling really full of himself. He is self-congratulatory about his own cleverness, and his arrogance causes him to make a key mistake. As they sail away, Odysseus shouts to Polyphemus to taunt him--and reveals his real name. In anger, Polyphemus prays to his father Poseidon, the god of the sea. Any other trials and tribulations that Odysseus goes through for the next ten years is because of Poseidon's wrath.
Throughout his adventures, Odysseus learns to become a more patient and careful man. Although he is still as clever as ever, he learns how to temper his arrogance in order to control the situation better. By the time he finally gets home to Ithaca, he is a changed man. He is no longer the hotheaded and proud young man he was when he left for the Trojan War, but a wiser person in every way.