Fifteen chapters of Huckleberry Finn is a lot of novel and
            many "conflicts" so I will only add a few to supplement the excellent answers already
            provided.  
One important conflict is symbolized by the
            contrast between the Widow Douglass and her sister, Miss Watson, who represent two types
            of Christians. The widow is a sort of idealized Christian who does good works and is
            full of Love: In many ways she represents the better side of our current philosophies,
            the ones which emphasize Jesus's moral and loving message and downplay the Hell-fire and
            damnation side of the equation.  Miss Watson is the opposite.  She represents a sort of
            holier-than-thou Christian (or any religious person) who believes that he or she is
            living in line with the rules of proper Christian behavior and that everyone else who is
            not doing the same is a sinner in God's eyes and is going to suffer eternal punishment
            in Hell after this life.  
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Sometimes the widow would take me one side and
            talk about Providence in a way to make a body's mouth water; but maybe next day Miss
            Watson would take hold and knock it all down again. I judged I could see that there was
            two Providences, and a poor chap would stand considerable show with the widow's
            Providence, but if Miss Watson's got him there warn't no help for him any more.
             (Chapter 3)
A very revealing
            conflict of sorts is revealed in the very next sentence where Huck concludes that he
            would be willing to "belong" to the widow's Providence "if he [God] wanted me" even
            though he can't understand why God would want an "ignorant" as well as "low-down and
            ornery" fellow like himself.  This conflict is perhaps a form of man vs. himself, for
            Huck, who is with the possible exception of Jim about the most moral person in the book,
            thinks of himself the way society sees his family, as white trash.  This belief that
            other people, people who are better educated, or go to school, or church, or hold jobs
            etc. are better people, and that God approves of such people and disapproves
            of people like Huck, well, that idea is at the base of the largest conflicts
            in the book.  After all, we must remind ourselves, that all the so called good,
            church-going, proper, moral, upright people in the novel, for the most part, either own
            slaves or approve of the institution of slavery.  For example, late in the novel, Tom
            Sawyer offers to help Huck in his effort to free Jim.  Well, Huck simply cannot
            understand this: To Huck, Tom is a good boy who should not be involved in such a
            seriously evil (in Huck's perception, which has been warped by his society) act as
            helping a slave escape: 
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Well, one thing was dead sure; and that was,
            that Tom Sawyer was in earnest and was actuly going to help steal that nigger out of
            slavery.  that was the thing that was too many for me.  Here was a boy that was
            respectable, and well brung up, and had a character to lose; and folks at home that had
            characters; and he was bright and not leather-headed; and knowing and not ignorant; and
            not mean, but kind; and yet here he was, without any more pride, or rightness, or
            feeling, than to stoop to this business, and make himself a shame, and his family a
            shame, before everybody. I couldn't understand it, no way at all.
             It was outrageous...   (Chapter
            34)
This passage reveals so
            much of what makes Huckleberry Finn the great American classic that
            it is.  Huck's sincerity and genuine good feeling, indeed love, in wishing to free Jim
            from slavery is the most moral and upright thing in the novel--yet he sees himself, and
            his plan to free Jim, as the exact opposite of that, as dirty, low, immoral, shameful,
            literally disgusting!  This is Twain's ingenious indictment of the Southern Society he
            was raised in--that it taught everyone who wanted to live in that society as an accepted
            member of the social world that slavery was good, and that those who opposed slavery or
            aided slaves in escaping, were evil--when Twain could see and wanted his readers to see
            that the exact opposite was true: That slavery was evil and that those who opposed it or
            aided slaves in escaping were good!  This conflict, that Southern Society was teaching
            that what we know  to be evil (slavery) was good, and what
            we know to be good (undermining slavery) was evil is the true heart
            of this amazing novel.  It creates the single greatest conflict in the novel, Huck
            versus himself, because Huck's natural goodness knows that the right thing to do is to
            set Jim free, but his conscience, which would normally tell a person what is right or
            wrong, has been warped by his Southern upbringing so horribly that he feels guilty for
            helping Jim!  Thus, in the greatest chapter in the novel, Chapter 31, when Huck decides
            he will literally go to Hell if that is the price he must pay for helping his friend, we
            should remind ourselves that Huck has been raised among church-going, strict Baptists
            for whom Hell is a real and terrible place--eternal damnation--eternal suffering and
            torture--a place where one burns forever!  How tragic, that a good
            boy, doing the right thing, should be made to feel that he is evil and degenerate for
            actions that are objectively moral!