How can you narrow it down??! Well, the conflict of social inequity is certainly at the forefront of this novel. The theme of justice certainly ties into this, as well. The Widow Douglas tries to instill christian and family values in Huck, yet she owns Jim and is treated as property. Ironically, Jim has the only true family and morally conscious family in the novel. Huck struggles with his own feelings of right and wrong on this issue, at times understanding the injustice of owning human beings, but breaking the law in helping Jim escape.
I agree that it would tough to label just one major conflict - I would add to the above answers the individual vs. society. This conflict is seen throughout the book in various circumstances. Huck choosing to help free Jim, Jim's escape, the attempted lynch of Col. Sherburn, the King and Duke's scams against the towns they entered. etc. One of Twain's purposes was to point out the hypocrisies in society, and he does this through this conflict.
The main conflict of Huck Finn is his struggle with his conscience. He has been raised with a certain set of values, and he struggles with those values when he goes against them. For example, when he helps Jim escape to freedom, he has been raised to believe that it's wrong to help a slave escape. He doesn't realize he's taken a stand against a society that condones enslaving others. He just feels he's "done wrong" because he didn't follow the beliefs that he's been taught.
You only want one? Then I'd say it is between forces that support civilization and forces that fight it. What makes the novel great, though, is that these are presented in such a complex and shifting fashion. At times Huck actively fights against being civilized; at times his great heart and his sympathy for Jim and others is the very soul of civilization. Likewise, stealing Jim is, technically, a crime, and an assault on American laws--but helping him be free fulfills the larger spirit and dream of American civilization.