The end where Chang is adopted after having helped stop Rastapopolous.
Hell, Tintin's interactions with him in general.
The Black Island
The titular island has a Gorilla who's sent to kill Tintin. It's injured and Tintin saves the animal, who then proceeds to become his friend.
Explorers On the Moon
Wolff's Heroic Sacrifice. Especially when Captain Haddock yells at the Thompson and Thomson duo not to say anything bad about Wolff.
The Calculus Affair
In The Calculus Affair Tintin and Haddock come across a scientist who's been attacked by someone impersonating Calculus and is understandably angry when Haddock tells him who they're looking for. He calls Calculus a monster and Haddock immediately objects that Calculus is his friend and he won't hear anyone else say such a thing about him.
Tintin and the Captain going through hell and high water to rescue Calculus. Notable for showing that despite Calculus annoying Haddock to no end, he cares for the old goat fiercely. In fact, in the latter album, when Haddock believes they will be able to rescue Calculus later that same day, he proclaims it to be the best day of his life.
Haddock: "Hold on Cuthbert. We'll find you!"
The Red Sea Sharks
Haddock goes ballistic when he meets a modern-day slave driver. While his anger is as always Played for Laughs, it's worth noting that one of his biggest fits of anger ever is caused by him seeing a man treating another man as an animal. Jerk with a Heart of Gold indeed.
Flight 714 to Sydney
At the beginning of Flight 714 to Sydney, Haddock notices a poor man at the airport and compassionately gives his hat back, with a $5 bill secretly tucked inside. Haddock thinks about how happy the poor man will be, until he discovers that he's a millionaire named Laszlo Carreidas.
Tintin in Tibet
Chang goes through a real Trauma Conga Line, having survived a plane crash with injuries. Then a Yeti takes him and while Chang thinks the Yeti's going to eat him, the Yeti actually brings him food so he'll get his strength back up. Then later in the story, he reveals that the Yeti picked him up and took him away from the previous cave because Tintin was coming to the crash site. The Yeti did this because he was afraid that Tintin and co was coming to harm Chang, so the Yeti was actually trying to protect Chang. After Chang is rescued and finally being taken to where he can receive medical attention, the Yeti's sad cries are heard (and by the characters as well!) because of the loss of the yeti's only friend. It ended well; but had they been unable to save Chang, he probably would have died in the mountains because the Yeti didn't know Chang really needed medical attention even though he had saved Chang's life. It also doubles as a Tear Jerker.
Another extremely heartwarming incident in the same story: Captain Haddock attempts to sacrifice himself by cutting his lifeline in order to save Tintin, who is tied to the other end and unable to pull Haddock up. If there was any doubt that Haddock is a heroic and loyal friend despite his vices, this scene obliterates it.
Tharkey coming back to rescue them should count as well.
Haddock repeatedly comes back after swearing up and down that Tintin was crazy for going off on his hare-brained rescue mission. The first time he surprises Tintin by recruiting an experienced Sherpa guide and several porters (and a rucksack full of whiskey), and the second time he shows up at a remote village, sheepishly explaining that he's only there to get a photo of the Yeti to sell to a magazine.
Haddock: *shows up with several porters* Dont say anything, I'm going whether you like it or not! *stomps past*
Tharkey: He is good friend.
Tintin: That he is.
The whole story is one long heartwarming moment. Tintin risks his life on a seemingly hopeless mission because he had a dream that Tchang was still alive, and yet his is not the most profound proof of friendship in the album. Captain Haddock comes along for practically every step of the way despite having never even met Tchang and not believing that he is alive at all. He goes on the journey nonetheless because Tintin is his friend. That is one of the most impressive feats of friendship in all of fiction.
Also a Real Life Heartwarming Moment: Hergé had used a friend he made while researching for The Blue Lotus, Zhang Chongren, as the basis for Chang Chong-Chen, a friend Tintin makes when he is in China. By the time Hergé wrote Tintin in Tibet, he had not seen Zhang for several decades, but the French media managed to find him and arranged a trip for him to travel to France, where the two friends finally met. There is a photo of the two of them sitting in front of a cutout of Tintin and Chang saying the words used in their reunion in that comic.
Tintin/Hergé: I knew I'd find you in the end!... This is wonderful!"
Chang/Zhang: "Tintin! Oh, how often I've thought of you!"
The Castafiore's Emerald
Haddocks noteworthy encounter with the Gypsies. Initially, he is confused by them staying in the trash, not understanding how someone would enjoy being there, only to quickly learn they have actually been forced here because nowhere else was allowed to them by the authorities. Disgusted by such a treatment, Haddock immediately gets angry as usual, and grants them permission to stay in a valley near Marlinspike Hall. When both Nestor and the authorities try to tell him this will bring him nothing but trouble, he shrugs this off and still insists they do so.