"I am afraid, my dear Watson, that most of your conclusions were erroneous. When I said that you stimulated me I meant, to be frank, that in noting your fallacies I was occasionally guided towards the truth. Not that you are entirely wrong in this instance." (1.17)
The very first scene of the novel quickly establishes the dynamic of their friendship. Holmes is superior and a bit condescending to Watson. He clumsily tries to express his appreciation for his friend's ideas. He's clueless that telling Watson that he's helpful mainly as an inspiration to his own genius might be a tiny bit insulting. By now in the Holmes canon, we know that Watson handles this kind of treatment with grace. Their relationship is too strong to be threatened by it.
"This family paper was committed to my care by Sir Charles Baskerville, whose sudden and tragic death some three months ago created so much excitement in Devonshire. I may say that I was his personal friend as well as his medical attendant. He was a strong-minded man, sir, shrewd, practical, and as unimaginative as I am myself. Yet he took this document very seriously, and his mind was prepared for just such an end as did eventually overtake him." (2.7)
Dr. Mortimer is an awkward character in the novel. He mainly serves as a human Exposition Fairy who fills in Holmes and Watson on the background of Sir Charles Baskerville and the Hound and then more-or-less disappears. Dr. Mortimer's friendship with Sir Charles is a plot convenience to give us access to Sir Charles' thoughts on the Hound. It also lets us know a little about what kind of person Sir Charles was.
"At the present instant one of the most revered names in England is being besmirched by a blackmailer, and only I can stop a disastrous scandal. You will see how impossible it is for me to go to Dartmoor."
"Whom would you recommend, then?"
Holmes laid his hand upon my arm.
"If my friend would undertake it there is no man who is better worth having at your side when you are in a tight place. No one can say so more confidently than I." (5.76-9)
Holmes really seems to trust Watson absolutely. He wouldn't send just anybody in his place to protect Sir Henry and report on the happenings around Baskerville Hall. On the other hand, Holmes is taking Watson for granted. While Watson's flattered, he's still taken completely by surprise when Holmes offers to send him off to Devon without asking him first. We assume that Holmes can be a pain to deal with as a friend. What if Watson had World Cup tickets for that weekend?
"You think, then, that some dog pursued Sir Charles, and that he died of fright in consequence?"
"Have you any better explanation?"
"I have not come to any conclusion."
"Has Mr. Sherlock Holmes?"
The words took away my breath for an instant but a glance at [Stapleton's] placid face and steadfast eyes of my companion showed that no surprise was intended.
"It is useless for us to pretend that we do not know you, Dr. Watson," said he. "The records of your detective have reached us here, and you could not celebrate him without being known yourself." (7.36-40)
There's a cool blurring of lines between the real and fictional worlds here, since Stapleton has read Watson's stories about Holmes ("the records of your detective have reached us here") much as we have. Stapleton emphasizes the fact that Watson and Holmes are compadres: where Watson appears, Holmes must also be in the neighborhood. And where Watson is investigating, Holmes must be operating in the background. Their friendship is as famous as Woody and Buzz, Thelma and Louise, Dawson and...well, you get the idea.
I am no antiquarian, but I could imagine that [these prehistoric people] were some unwarlike and harried race who were forced to accept that which none other would occupy.
All this, however, is foreign to the mission on which you sent me and will probably be very uninteresting to your severely practical mind. I can still remember your complete indifference as to whether the sun moved round the earth or the earth round the sun. Let me, therefore, return to the facts concerning Sir Henry Baskerville. (8.2-3)
Watson enjoys admiring the barren landscape of the moors and the prehistoric huts and ruins that dot the area. But he knows Holmes would think that daydreaming about the lives of cavemen is a waste of time. Even though Holmes and Watson aren't literally talking to each other, we still get the flavor of their teasing relationship from Watson's letters from the country.
"And then again, sir, we were both of us very fond of Sir Charles, as we well might be considering all that he has done for us. To rake this up couldn't help our poor master, and it's well to go carefully when there's a lady in the case. Even the best of us—"
"You thought it might injure his reputation?"
"Well, sir, I thought no good could come of it. But now you have been kind to us, and I feel as if it would be treating you unfairly not to tell you all that I know about the matter." (10.43-5)
Conan Doyle writes at a time when it's still common for people to employ servants. This exchange with Barrymore shows readers the benefit of treating your servants kindly (beyond the fact that it's the right thing to do, of course). Barrymore's loyalty to Sir Charles makes him protect his reputation by not revealing his secret meeting with a woman the night he died. And now, Barrymore's gratitude toward Sir Henry makes him reveal the secret. Since the mysterious woman is key to the case against Stapleton, Barrymore's decision to open up to Sir Henry and Watson turns out to be very important.
For a moment or two I sat breathless, hardly able to believe my ears. Then my senses and my voice came back to me, while a crushing weight of responsibility seemed in an instant to be lifted from my soul. That cold, incisive, ironical voice could belong to but one man in all the world.
"Holmes!" I cried—"Holmes!"
"Come out," said he, "and please be careful with the revolver."
I stooped under the rude lintel, and there he sat upon a stone outside, his gray eyes dancing with amusement as they fell upon my astonished features. […]
"I never was more glad to see anyone in my life," said I as I wrung him by the hand. (12.1-5)
This reunion between Watson and Holmes is the real emotional climax of The Hound of the Baskervilles. The case is interesting, and we're glad that Stapleton doesn't get away with murder. But the friendship between Holmes and Watson is where all the positive feelingin the novel really comes from—it's nice to see the old team get back together.
"But why keep me in the dark?"
"For you to know could not have helped us and might possibly have led to my discovery. You would have wished to tell me something, or in your kindness you would have brought me out some comfort or other, and so an unnecessary risk would be run." (12.27-8)
Even with his best bud, Holmes can't turn off the part of him that plans and schemes, which leads him to manipulate Watson almost as much as he does the other characters in The Hound of the Baskervilles. This hurts Watson's feelings, but he eventually comes around to understanding and even agreeing with Holmes that the case comes first. Like we said, a challenging friendship.
But first I had the unpleasant duty of breaking the news to Barrymore and his wife. To him it may have been an unmitigated relief, but she wept bitterly in her apron. To all the world he was the man of violence, half animal and half demon; but to her he always remained the little wilful boy of her own girlhood, the child who had clung to her hand. Evil indeed is the man who has not one woman to mourn him. (13.21)
Mrs. Barrymore's grief over her baby brother's death, even though he was a murderer who ruined her family name, shows the connections that exist between people even under the most extreme circumstances. However, this little note at the end that, "Evil indeed is the man who has not one woman to mourn him" also appears to foreshadow Stapleton's death. By the end of the novel he's managed to alienate both his wife Beryl and his lover Laura Lyons. Even Selden has Mrs. Barrymore to mourn him. Stapleton has no one.