Luke Skywalker remains the most popular character in Star Wars, with fan allegiance greater than that of Darth Vader himself. That's all due to a set of specific character traits that helped establish his character's story arc, and journey towards becoming the savior of the Jedi Order.
Some of these traits waned over time, only showing in his earlier years, while others were cultivated as he grew into adulthood. Some persisted, much to his own detriment, which showed that despite his iconic status and powerful connection to the Force, he was still a deeply flawed human being.
His Immaturity
Luke started out as a relatively immature young man who was too busy dreaming of galactic adventures, at the cost of the moment. This kind of childish behavior stuck with him until he was thrust into the conflict between the Rebellion and the Empire, where he was forced to grow up quite fast.
Without the tutelage of his mentor Obi-Wan Kenobi, Skywalker set out to find Jedi Master Yoda, whom he believed could complete his Jedi training. However, Yoda easily played on his immaturity and petulant behavior in order to teach him a valuable lesson about responsibility as a Jedi.
His Lightsaber Prowess
Though not formally trained by any Jedi Master, Luke was nevertheless proficient in lightsaber combat, perhaps due to his natural affinity with the Force. His technique most closely resembled that of Form V, the so-called "Perseverance of Form," which prioritized heavy attacks, and blaster deflections.
This is why Luke found it so easy to gain the upper hand against multiple opponents wielding blasters. Form V melded well with Luke's approach to combat situations, which was primarily based on defense first, then a counterattack. Luke trained a number of powerful Expanded Universe Jedi in lightsaber combat, as well as a new crop of students in Disney's sequel trilogy.
His Piloting Skills
Much like his father, Anakin, Luke was an expert pilot who cut his teeth blasting Womp Rats in his T-16 on Tatooine. By the time the Death Star was looming over Yavin 4, he had all the training he needed to dive into its trench, and take it out with a pair of proton torpedoes.
His later years would focus less on flying, and more on his fledgling Jedi Academy, but Luke never lost his skills. This was tied not just directly to his own character, but that of his father, signifying a connection based on a very torrential bloodline.
He Knew His Limitations
While Luke did possess incredible power within the Force, he also knew what he could, and could not do. For instance, he was a remarkable diplomat, but he tended to shy away from military strategy. He was therefore a leader in some ways and a follower in others.
This was actually a good thing, as it prevented Luke from falling victim to his own sense of grandeur. As he continued to rack up victories, his galactic reputation began to soar, and this emphasized the need for him to know his limits and play within them.
He Second-Guessed Himself
Luke may have been one of the most powerful Jedi in history, but he didn't always think so. While he knew what he was capable of, he was much more fearful of whether his abilities would lead him down a dangerous path. As such, he tended to trend with considerable caution.
This was true not just in the Expanded Universe material, but also in Disney's canonized chronology when he exiled himself in a moment that caused many fans to hate Luke Skywalker. He may have thought it was for the good of the galaxy, but his lack of confidence caused more problems than it solved.
He Was Compassionate
Luke Skywalker did many nice things for people over the course of his life, exercising compassion as much as he could. Even in the face of danger, he tried to see things from the other perspective, and that helped him establish peaceful relations with many cultures, such as the Ewoks of Endor.
It was that compassion that also helped drive his determination to end the Empire's reign of terror. He knew that as long as the cruelty of the Empire was allowed to continue, trillions would suffer as a result, and he couldn't bear the thought of it.
His Moral Compass
Luke could tell right from wrong quite easily, perhaps because his moral compass allowed him to see things in black and white. However, he did have trouble identifying the various shades of grey in between, such as the Jedi Order's role in galactic affairs and the rise of Darth Sidious.
Regardless, Luke would attempt to pursue a moral path wherever possible, even if it meant flirting dangerously with the dark side in order to get there. He ignored Obi-Wan Kenobi's recommendation to kill Darth Vader outright, instead pursuing a more dangerous path of redemption, which nearly cost him his soul.
He Was An Idealist
Luke was an idealist, even in his earliest days. It was this idealism that would eventually lead to his undoing, following his nephew Ben Solo's fall to the dark side, and ascension as Kylo Ren. However, it was a major character trait that defined Luke, right to the end.
At every possible opportunity, Luke pursued a path that he believed would lead to happiness for everyone. That included battling the fascistic Galactic Empire, ridding the galaxy of the Sith, or helping to establish peaceful relations with countless worlds.
He Was Impatient
Luke's impatience was a dangerous warning sign that almost threatened to derail his life. It was the same kind of impatience that drove his father, Anakin, closer and closer to the dark side of the Force, and eventually, his own downfall.
This was perhaps his most insidious character trait, and one he spent a considerable amount of time trying to get a handle on. He'd later recognize the value of patience, as stressed by his tutors Obi-Wan Kenobi and Yoda, but the path to get there was wrought with tragedy, including the loss of his own hand.
His Courage
Luke was courageous, almost to a fault, and he would rush into danger if he believed it was for the right reasons. He showed remarkable bravery in the face of Stormtrooper battalions, his duel with Darth Vader, and his mission to destroy the first Death Star over Yavin 4.
Each of these times, fear should have overwhelmed the young man, but he stuck to his principles and did what he had to do. The number of times Luke rubbed shoulders with dealt is incalculable, but his inherent bravery helped him survive each time.