Much is made of George Lucas’ homage to Joseph Campbell and Luke on the classic hero’s journey. But what about Han? Han is on a journey of his own, a somewhat different quest with a somewhat different goal. Han is jaded and world-weary, unlike Luke and Leia who are fresh and full of passionate conviction. Han considers them naïve at the same time he admires them. He wants to believe in something, if only there were something to believe in. That is his quest. He is looking for something to believe in, something to give his life meaning. 
His journey starts with a call from Obi-Wan, which he accepts, not for purpose but for payment. As Luke answers his own call, Han meets his every step with doubt and judgment, and yet he follows everywhere Luke goes. He wants so desperately to believe. Protesting the whole way, he accompanies Luke on the road of trials, through the belly of the whale, guided by proxy by Obi-Wan, meeting up with his very own personal goddess, Leia. And though Luke and Leia become his companions, let’s not forget his one true friend, Chewbacca, who follows him through every trial, no matter what the cost. Also, while Luke has his light sabre, Han has the Millennium Falcon as his special token of power. All the pieces are there and they all fit together to make the perfect picture. 
Ultimately, after all of his trials, he decides to take his reward and flee the scene. But he just can’t do it. He is so close to obtaining his goal, so close to being part of a group with a greater purpose, a greater faith, that he has to come back, rushing in to save the day so that Luke can do what he must to save the rebellion. Han has achieved his goal. He has found something to believe in and people who can give his life meaning. 
Put in this format, Han’s hero’s journey is just as classic as Luke’s. Joseph Campbell would be proud.
There are probably more well-versed nerds than I who might correct me, but as far as I can tell, Han was the first (or at least one of the first) characters in space sci-fi to be an anti-hero, a not so nice good guy.
At first, you had Star Trek – highly organized, everyone polite and wearing the proper uniform. Then along comes George Lucas, introducing the possibility in space, there might actually gangsters, smugglers, and intergalactic organized crime.
Han certainly had questionable morals going in, and I absolutely agree that one of the attractions of Star Wars is its “lived-in” feeling. I do think that he turns out to be a very good guy, if a tad reluctant. As he tells Princess Leia he’s a “scoundrel” and a “nice man” both at the same time. In fact, if he hadn’t returned to protect Luke, Luke wouldn’t have been able to destroy the Death Star, thereby striking an important blow against the Empire. Therein lies his hero’s journey, even though he doesn’t fundamentally change his personality.
Star Trek does feel a little sterile by comparison, doesn’t it? And I say that even though I like Star Trek a lot.
Thanks so much for your comment!