One scene that really struck me was the conversation between Huck and Jim about King Solomon and King Louis of France. Huck tries explaining the details of both kings to Jim, and Jim just contradicts him with uniquely logical arguments the entire time. My favorite is when Huck tells Jim that King Louis speaks French. That makes no sense to Jim, and he asks Huck if a cat is a man, or if a cow is a man. Huck responds no, so Jim says of King Louis being a man, "Dad blame it, why doan he talk like a man? You answer me dat!" (Chapter 14).
Another funny scene occurs when Jim is going to use his ox's hairball to tell Huck's fortune. Unfortunately, the hairball "wouldn't talk without money." So Huck gives him a counterfeit coin, and all of a sudden, the hairball can talk. (Chapter 4) It is a funny scene because first of all, a hairball? Secondly, money was required for a fortune.
One last scene that comes to mind is the scene in which the boys are planning their kidnapping and robbery adventures (chapter 2); they have no concept of what they are even trying to do. They figure that taking someone for ransom means that "we keep them 'till they're dead." Then they figure that with kidnapping women, "by and by they fall in love with you and never want to go home no more." All in all, it's a hilarious scene of boys naively planning mischief.
These are just three scenes among many; Twain does a great job making the book humorous.