The main character's possession of a strong will, above and beyond all other qualities, is a trope for a reason; it reinforces what we all want to believe. Rather than being limited to our inborn talents, or even the fruits of our experiences, we like to believe that we can accomplish things simply by virtue of how badly we want them. It's a dangerous idea, because there's a lot of truth in it, but putting too much faith in it virtually guarantees that it will never work for you. You can't really reason yourself into having a strong will, it has to come from something more primal. The possibility of deliberately turning yourself into a strong willed-person is dealt with extensively in Tengen Toppen Gurren Lagann, but, one problem at a time.
So often, anime asks me to believe that a character has an incredibly strong will; that's why they can accomplish great feats, despite all odds. Usually, I accept this as a viewer- I know the show wouldn't work otherwise. However, while I've always dutifully accepted it, with Clare from Claymore, for once I actually believed it.
Hit the jump for more about Clare, and my belief in the Clare that believes in me, or something. Damn Gurren Lagann.

If you haven't seen Claymore yet, I'm not sure whether or not to recommend it. Obviously I have a pretty high opinion of it- although the non-Clare elements do bring it down a few notches. But the fact is it's an extremely dark, depressing series, and at some point while watching the show, I wished I had never started it. Claymore gives me characters I want to remember, in a world I'm desperately trying to forget, for the sake of keeping the nightmares at bay. Admittedly, one of the reasons that Clare stands out as a protagonist is that she just has so much to overcome. I think she would laugh at what 99% of all anime characters deign to call "problems."
The capping off of what I'm sure was a WONDERFUL childhood.
In Clare's reality, a small group of female warriors are in charge of keeping a world teeming with monsters at bay. Unfortunately, the only way to produce warriors strong enough to fight the monsters is to turn people into half-human, half-monster hybrids. Aside from the fact that there's obviously some wickedly painful surgery going on there, this practice has many other drawbacks. Nevertheless, these warriors keep the monster population at bay. Thanks to their work, most people can lead normal, relatively monster-free lives. For the Claymores themselves, their role deprives them of anything resembling normalcy, or even much of an identity. One of the first things we learn about the group is that they weren't the ones who named themselves Claymores- it's basically a slang term, something other people started calling them based on the swords they wield. They couldn't be bothered to name themselves anything.
In a situation like this, it's not surprising that some of the Claymores are...uh...well, unbelievably bitter fucking bitches. Teresa, the strongest Claymore, is borderline sadistic when dealing with the humans that she's supposed to be saving. After killing a bunch of monsters, terrorizing the townspeople in the process, she even kicks a little girl who only wants to hug her. She continues to reject the persistent little girl, who follows her out of town and into the wilderness. We don't blame Teresa; she didn't create this world, and she suffers from it as much as anyone. If anything, her absolute rejection of Clare is done out of a kind of tough love- she wants Clare to forget her and learn to deal with her life, such as it is. Ironically, when Teresa kicked Clare, that was the beginning of her demonstrating respect for her. You can almost hear her thinking "Look, I don't normally kick kids, but you're so persistent I don't know how to get it through your thick skull any other way."
I see your rejection, and I LAUGH.
Clare, through either intuition, wishful thinking, or a combination of both, believed that Teresa did have a kind nature, and her callous behavior wasn't indicative of her true feelings. We later learn that she was following Teresa primarily for Teresa's benefit- she believed so strongly in Teresa's hidden, vulnerable self, that she could put the needs of that person above herself. On some level, she knew that she was powerless to help herself, but that her support could mean something to someone else. Ultimately, whether she had those inclinations or not, Teresa started believing that she had a kind nature herself, because Clare's absolute belief was contagious. At the time, Teresa was the most powerful woman in the world, and Clare had no power beyond her own will, but it was Clare who molded Teresa into what she wanted her to be.
Obviously, Clare's transformation of Teresa demonstrates the power of her will. However, her will makes it's presence known in other ways. When Teresa jumps off a cliff, thinking she's finally shaken Clare off, Clare actually throws herself face first down the cliff with only the slightest hesitation. It's not that she's a robot, and jumped off without thinking: you can see that she takes a brief moment to think about it, and then jumps. Were I in the same position, with my toes hanging over the precipice, I don't think I ever could have jumped. I don't think my force of will would ever be powerful enough to overcome the primal fear of death. That incredible mind-over-matter capacity was what convinced me of Clare's inner strength, and sold me on the character completely- because someone who can do that can do anything.
The way she falls down the cliff makes her survival look plausible, by the way. Maybe unrealistic, but plausible. That's all I ask.
I can't relate to ninja jutsu, special attacks, and most of the things that anime characters do- when the story tells me that the character is doing something scary or difficult, I shrug and accept it. But throwing yourself face-first down a cliff? That I can relate to; that shows me how the character in question is different from myself. It shows me why she's the main character. Later, when the adult Clare does start to use more typical super-powered techniques and struggles to grow stronger, I believe in the legitimacy of her struggle, because I've already been shown what she's made of in terms that I can understand. And when it inevitably turns out that Clare is a special Claymore, "The One" if you will, I don't mind it; I don't feel like the writers are forcing a cliche on me with no justification. They've earned the right to use that archetype, because they've shown me that it's just; they've shown me that the character deserves it.

I would like to give the animators extra special kudos for the "you've got to be fucking kidding me" attitude that Teresa has throughout this sequence.
In short, whenever someone tries to convince me of the limitations of fictional characters, or the inability of fiction to transcend cliches. I think of Clare. That's how she's changed me.
Now, look who done growed up! Uh, I'd be careful if I were you- the badass be strong in this one.