Unmarked spoilers ahead!
Shirou's Endings, Perspective One: The Three Acts of Man
The three routes of Fate/stay night can almost be seen as a trip from the Ideal end to a bit closer to the Cynic's side of the Sliding Scale of Idealism Versus Cynicism. Many fans describe it as akin to the journey from child to man.
In Fate, Shirou remains a child in many ways, facing the future with his ideals unexamined and uncompromising. His love for Saber is a very Fairytale like thing; indeed, in later remakes they are given a distant, but very fairytale like ending.
In Unlimited Blade works, we see a world view many would see as young adult— the view of a teenager who wants both the ideal and reality. Even though he's been shown the faults in his hero of justice ideal, he decides to pursue it anyway— a struggle, to be sure. Here, Rin and her Cynicism serve to balance his idealism.
In Heaven's Feel, reality and Sakura drive Shirou toward a more adult viewpoint. Here we see him (as a certain tiger once suggested) holding fast to what he can, and compromising when he must. This is more mature than he can bring himself to be in the other ends. His father was right, you can't save everyone— and so he will save what is important to him.
Shirou's Endings, Perspective Two: The Problem With Selflessness.
Many, both here on TV Tropes and elsewhere, have noted the fact that Shirou doesn't place much value on his own life. In fact, it is this that allows him his amazing use of projection magic.
But the three routes also show a change in this. In Fate, Shirou's ideal remains, as does his selflessness. He has the naive devotion of a fairytale hero, and it earns him (at best) a distant, fairytale, dreamlike ending with Arturia.
In Unlimited Blade Works, we see a Shirou who is less naive, but still clings to his ideal. In other words, what he experiences grants him enough self-awareness to acknowledge reality— and be stubborn in the face of it. Indeed, it is likely that here, Rin will be the "adult" in the relationship.
Finally, Heaven's Feel. While there is no doubt that Shirou is Sakura's hero here, we also see him asserting something he wants. In the better endings to Feel, Shirou puts Sakura's well being before his dream, before anything else. This is not merely limiting his dream to just being Sakura's hero. This is deciding he wants her. A selfish desire, even if his love drives him to great heroism— but that's actually the point.
While Shirou does noble things in the other routes, it is also there that most events that cause much of his labeling as The Scrappy comes in. It's why Anime Shirou is one of the least liked versions— he's mainly based on Fate route, the one where he gets the least development. But by Heaven's Feel True End, we see a Shirou who can say, "No. I want Sakura to live." This does not doom him. It redeems him— asserting a selfish desire gives him a focus. Nor does it destroy his Projection ability— he can now direct his selflessness to something (and someone) he values, making him not a boy with a vague ideal but a man with a true cause— and a stunning skill to back it.
Shirou's Endings, Perspective Three: How much does it take to break a man?
Personally, I am amused at a great number of the interpretations of Shirou. Many have ascribed to the viewpoint that the Fate -> Unlimited Blade Works -> Heaven's Feel route progression shows Shirou's development as a person. The above analysis entries describe it in great detail.
A counterpoint that it seems not many have considered: Perhaps the three routes show the slow slide of the determined selfless idealist (a development end-goal of a great number of philosophical and religious systems) to a selfish cynic (the "base state" of humanity according to many philosophical and religious systems.)
In the Fate route, Shirou refuses to let go of his ideals, and his love for Saber. Shirou faces down Angra Mainyu, the personification of All the World's Evils, with nothing more then sheer willpower. His heart enters pure, and emerges untainted, despite witnessing all the ugliness and hatred humans are capable of. He refuses to drown in his ideals, and in the end manages to reach the Everdistant Utopia, reuniting with Arturia in Avalon.
What the distant finale means is that, despite everything the world could throw at him, Shirou emerged unscathed. He lived his ideals as best he could, and grasped his reward by entering Utopia (The absolute endgoal of every religion ever: To cast off sin, and be allowed into heaven). Fate/Shirou accomplishes this... and is often cast as being the least developed of the three.
In Unlimited Blade Works, Shirou's ideals begin to waver. He begins to develop an ego to supplant the super ego he had been operating primarily on. In this route, Shirou does not face any true and major tests of his ideals. He is never plunged into the muck of the grail, which I doubt UBW/Shirou could have survived. This Shirou begins to yearn, his selflessness begins to slip. He wants everyone to be happy, but he also wants Rin (and Saber, in the good end) to be happy. This places a strain on his ideals: Whose happiness does he value more? Humanity's, or Rin's (and Saber's)? Shirou slides further away from enlightenment/salvation/whatever, but he never falls. When he is faced with Archer, the manifestation of his ideals betrayed, he catches himself. He truthfully examines his ideals, and comes to a conclusion: He will strive for both. He will save as many as he can, and he will be happy with saving as many as he can.
I feel UBW/Shirou is the best most humans can achieve. He slips from enlightenment, but stops his descent, and begins to pull himself back up. He never reaches that everdistant utopia, but he lives as best a life as a man is able.
Heaven's Feel finally breaks him. HF/Shirou is a straight freefall from Saviour to Man. In Heaven's Feel, Shirou not only yearns, but he places his yearning, his desire for selfish happiness, above the happiness of the world at large. HF Shirou regress to the origin point of Man, having reached the bottom rung of enlightenment. His Ego firmly supplants his super ego, and his even his id shows up every now and then. Shirou chooses Sakura, the one thing he wants, over the world and his ideals. If his ideals require that Sakura die that the many be saved (the infamous Mind of Steel ending that people go frothy-mouth over), then he chooses to abandon his ideals. To embrace selfish wants, and do what is best for himself and those he places value in.
HF/Shirou is perhaps the most human of his incarnations. The majority of people on this planet choose, every day, to put themselves ahead of strangers. To put friends and family ahead of the unknown and unknowable others they share the world with. Perhaps this is why people like HF/Shirou. Because his weakness remind them of their own weakness. Because they can empathize, and understand this one choice, as they couldn't grasp the absolute selflessness of Fate, or the more contained but still-present drive to save people of UBW.
The Routes signify how circumstances make the man
The way the storylines diverge in each route showcase the importance of context and circumstances in determining what is the right thing to do.As has been stated, the Fate route sees Shirou sticking to his romantic ideals. Unlimited Blade Works points out the flaws in Shirou's values without him abandoning them altogether, and Heaven's Feel has Shirou prioritize Sakura's life over his prior ideals, giving into his selfish desire to save the woman he loves.
In all three routes, the healthiest option for Shirou is determined by the circumstances he finds himself in.
The Fate storyline goes out of its way to enable Shirou's idealism. His love interest is the Knight in Shining Armor Saber, the stakes are very clearly black and white, and Shirou has a rock-solid support system that he can leverage to win the war and save the world. The "right thing to do" is never really in question, as all of Shirou's arguments with Saber and Rin about putting himself in danger, or Saber's own self-loathing become moot points when Kotomine shows his true colors and the Grail's true nature is revealed. The path forward is simple and obvious, leading to a truly righteous finale and resolution. It's telling that Saber is the one who gets the lion's share of Character Development, which ultimately amounts to her moving past her self-doubt and taking solace in knowing she did the right thing. Shirou and Saber are ultimately rewarded for their unerring righteousness in Realta Nua by being reunited in Avalon, a clear parallel to the promise of heavenly salvation found in many religions.
In Unlimited Blade Works, the cracks start to show as Shirou's support system is fractured with Rin not moving in as his tutor, and more significantly, The Reveal of Archer's treachery. In this route, it's spelled out quite bluntly how unwavering idealism, rather than being rewarding, can become an Ironic Hell. Archer is what Shirou would become if he forsook all his mortal attachments in service of his ideals; a man trapped in a brutal, thankless cycle of saving the world from its lowest points over and over again, with none of the human connections that make such a heroic pursuit worthwhile. Heroism itself loses all its value if it's divorced from the humanity innate in all of us.
Shirou can no longer afford to be an unwavering romantic; the disastrous consequences of doing so are staring right at him. But he still chooses to fight back against Archer's bitterness. Even with how flawed his values are, even with the manifestation of his potential regrets staring right at him, he's not going to throw it all away. He won't admit that he was wrong to have those ideals in the first place. Even if Shirou can't blindly follow in Kiritsugu's footsteps anymore, he can still strive for greatness nonetheless.
After all, while Rin isn't a king of legend like Saber, she herself is an aspirational figure, determined to uphold her family's legacy and become a better mage. She's very much human, but nonetheless the kind of person many others look up to. And this grounded, yet aspirational life is what Shirou now aims for.
Heaven's Feel explores the circumstances in which clinging to high-minded ideals is no longer feasible. The main love interest of this route, Sakura Matou, was robbed of her fairytale ending from the very beginning. Abused by Zouken Matou and groomed as a vessel for the Greater Grail, all so he could supplant the Einzberns and gain immortality, she was always a pawn in a bloody, horrific game played by one of the biggest monsters in the story. By the very nature of her upbringing, she becomes more dangerous the closer Shirou gets to her, as her love for him lowers her defenses, which both Zouken and Angra Mainiu exploit to make her to their bidding. Shirou's support system is more broken than ever, with Saber getting corrupted by Angra Mainiu and Rin getting increasingly cold and distant thanks to her own complicated relationship with Sakura. The price of his ideals is higher than it's ever been. Shirou has no one left to support him, or reward him. Sticking to his romanticism would require severing all his attachments and forsaking everyone he's known and loved, something he does to horrific effect in the "Mind of Steel" bad end.
Therefore, for his own happiness and salvation, he needs to disregard the needs of the faceless many and prioritize the woman he loves the most. Sakura's happiness becomes his happiness precisely because both of them need each other to save themselves. Ultimately, there is no happy ending awaiting those who give up on the people they love, which is why Shirou's salvation lies in doing everything he can to save Sakura from the hell she grew up in. No matter how difficult, reckless or foolhardy it is.
It's easy to stick to your ideals when the people around you embody those very ideals themselves. It's possible to bounce back from moments of doubt when you have a kindred spirit willing to work through those doubts with you. But if the price for your ideals is walking alone and leaving your loved ones behind, there is no happiness to be found on such a cruel road.
The Love Interests as Signposts in a Hero's Journey.
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