Here's the problem: Everyone assumes that they can simply pinpoint every action or description to a single, defined alignment per the rules. If only it were so easy... but it's not. You must account for motivation and intent by one's actions; not just actions alone. That's why there are so many different answers being offered, and in all likelyhood, more than a few correct, but differing answers as well. I can give you another estimation based on my own ideas, but that resolves nothing. Instead, here are a few things you need to consider, and perhaps the original author could provide some more information as it is needed.
He would never harm a child or defenseless person.
Why not? Because he is morally decent, or because he believes it is bad karma that could come back to him? It's obvious that he seems to protect the innocent, but brutally punishes the guilty. This would generally suggest that he is generally Good, but again, motive needs to be defined better. Why would he never harm these people? And more importantly, to what extent does he define a child or a defenseless person? Is the farmer who bravely defyies him from entering his house no longer considered defenseless because he is armed with a weapon? More definition is needed here.
He wants to save the world from a tyrannical and thoroughly evil organization.
Again, what is his motivation for doing so? Does he fight for the oppressed people of the land, or does he just want to take it's place instead? Maybe he's out to prove something to himself or everyone else, seeking the fame and renowned of becoming a hero. Does he have a personal vendetta against this organization, perhaps? Motivation reveals a lot.
He'll give the shirt off his back to a stranger if that would help them.
So you're saying he is generous and gives of himself. That seems pretty straightforward. And you're certain he'll do this everytime, or just with people he judges first as 'needy' and 'deserving'?
Staunchly loyal to his friends.
This defines a quality of the character that is not restricted to a single alignment, and thus has little bearing in this exercise. Most people who are truly friends with others tend to be loyal to them. Alignments will simply define the extent and the manner of their loyalty.
Won't keep rewards from quests, preferring to give it back to the town or to another worthy cause.
See, this is where you're just painting an obvious picture of someone who is clearly selfless and generous beyond reproach, but then you've added these other traits that are highly questionable. Up until this point, without any other information provided, he is clearly a person of Good alignment. But I must stress again, that without a clearly defined motive, we're only assuming such. Is he really Good, selfless, and generous by nature, or is there some other reason he behaves this way?
Uses torture as his primary questioning technique for prisoners.
And here we begin to see his other side, or his 'dark half'. What I want to know is, how does he feel about committing such actions? Is it a 'necessary evil' to do what is needed for the good of the innocents in danger? Or is it just a method he prefers because it gets results? Motivation and intent define alignments better than actions alone.
Has, on several occasions, beaten someone to death with their own limbs. (This was their punishment for a crime, most likely hurting children or the defenseless.)
That is an extremely brutal and violent act for any 'Good' person to commit. He may have Good intentions at heart, but his methods suggest there is a level of Evil that he is comfortable with.
A fervent believer in eugenics, he has sterilized many useless or stupid people along his travels.
What is his definition of "useless or stupid people"? This character seems to have placed himself on a very high and righteous pedestal to pass judgement on others, and more so to execute what he deems is the appropriate punishment based solely on his perceptions. A lot more detail on circumstances, motivation, and intentions would help paint a clearer picture regarding the methods of his madness in this case.
Seduces women in every town he comes across, hoping to sire an army along the way (ala Ghengis Khan).
This seems to have little to do with alignment and more to do with some kind of dementia. Is he keeping track of all the little bastards he's producing? Seriously, he would have to plant his seed quite frequently and throughout many far-reaching locations to infect the region with his own personal army. And you really must wonder, what is he thinking? Assuming this long-termed scheme of his actually works... what does he want with an army of his own? If he's so good and righteous, why doesn't he expect people to follow him loyally after all his efforts? This, above all else, seems to make the least bit of sense given all the other details provided about this character.
Without any further explanations given, I can't even guess what alignment really suits him. Depending on what is revealed by his motivations, I might venture to say that he's either Lawful Neutral or Chaotic Neutral. Hard to say which way, at this point.
