The end of Book 6 has a story where Doraemon have to go home. To prove that Nobita can stand by himself, he decided, no matter how bad it is, to fight Gian. He succeeded to make Gian running away in shame, while Nobita had to be carried home. The story ends rather tearjerkingly as the drawer Time Machine turns into a regular drawer...
But then, the next volume has it that Doraemon left a box shaped like himself, containing a drink called "Lies 800" in which anything spoken is a lie. After getting lied to badly by Gian and Suneo, Nobita exact his revenge to Gian and Suneo, and after that, Nobita spoke that Doraemon did not exist. Thanks to the effect of "Lies 800", Doraemon actually returned, and Nobita tearfully hugs Doraemon while proclaiming "I am so unhappy that you won't be at my side forever!"
The whole story was made because during the magazine era, Doraemon's popularity was thought to be waned that until positive feedback shows that the readers really missed Doraemon.
The story above was adapted into the "Stand By Me" CGI movie as the last segments.
In the episode "Two Shizukas", Nobita is stuck at identifying which is the real Shizuka and which one is copy. Cue Armor-Piercing Question.
Nobita: D-Do you like me Shizuka!?
Copy!Shizuka: W-What are you talking about!? Who would like someone like you!?
Real!Shizuka: Err..umm.. (blushing)
The episode "Doraemon's Time Capsule" (English dub) has two extremely powerful moments. The first, is when Noby and Doraemon are about to be incinerated, and Doraemon tells Noby to leave him behind as Noby can save himself, and Doraemon can be replaced. Noby tearfully refuses as he doesn't want to lose his friend and desperately keeps digging Doraemon's pocket for something to save them. The second is, at the end, when we find out that Noby arranged for a letter to be addressed to the newly made Doraemon, which said "Happy birthday, from your best friend forever," making the young cat-robot cheer. Doraemon realizes it was the letter Noby sent him that made the day he was born so special. As Noby said himself, "Whenever I can do something stupid that'll make you happy, I'll be there." It really is moments like these which make you understand why these two are best friends.
In general, the fact that everyone accepts Doraemon as one of their own, and especially that the Nobis accomodate him like a second son is pretty touching. This is the very definition of open-mindedness.
Heck, in the "Robot Kingdom" manga, at least, Nobita's mom explicitly says that Doraemon is also her son!
The short movie "Doraemon: Nobita's the Night Before a Wedding" has several, from Nobita and Shizuka trying to take the cat to her family who is about to move to America to the talk between Shizuka and her father, but the wedding sequence in the ending tops it all; especially with this song playing. It can (or will) make you cry happy tears.
Adult Nobita deserves some love as well, especially during the "Shizuka's present is Nobita" episode. Though he hasn't changed that much in 25 years (personality wise), the way he cares that much of his wife tells that he can go even back in time to don't make a mistake that would ruin their marriage.
The part when he interacts with the younger version of his Shizuka, by telling her that her "future prince", while the opposite of what she likes in a guy, he (himself) would improve himself by working hard enough to "grant that dream of hers, little by little" because he will love her.
From that interaction alone, Shizuka lends him the handkerchief that he made for her in the past, but never returns it to her. In the future, he finds it in one of his pockets, until the moment that the adult Shizuka recognizes it, while realizing that the man she interacted with 25 years in the past was not only her "future prince" but the adult Nobita, as well.
Say whatever you want about Gian, but you cannot deny the love he has for his younger sister, Jaiko. He has tried to help her anytime when she has trouble, from the moment he wants to show the "great amazing artist" she is to the world (even if he menaces the other kids of the neighborhood), or when she is dealing with love problems.
Nobita comes back in time to the day he was born and listens in on her mom and dad voicing their hopes for him. The next panel we see him staying up late to study—to the point that even his mom and dad tell him to give it a rest already.
A singer from Hong Kong made a song about the manga. For those of you who don't speak Cantonese, it is about Nobita's love and friendship for Shizuka and Doraemon and how he cares about them.
A special episode has Denja, a criminal robot, switching bodies with Doraemon during a check-up in the future. He turns out to be a very lonely Anti-Villain who never before has seen somebody as kind as Nobita. He even teaches Nobita to play baseball as well as winning the game for him! In the end, he cried Manly Tears as everything resolves to normal.
Previously, Nobita was looking for a red marble while Doraemon unintentionally crashes with Nobita, spoiling the Dorayakis Doraemon's carrying. While undoubtedly straining their relationship for awhile, Doraemon, in Denja's body, looking for a red marble at a dump in the future. Turns out, the red marble is for Nobita's sincerely-made birthday present, a clay model of Doraemon.
In "Doraemon: Nobita's Three Visionary Swordsmennote Nobita and the Three Musketeers", the fact that the movie hinted that Shizuka dreamed about that Nobitania and Princess Shizukaria get married to the end deserves a lot.
In "Doraemon: Nobita in the Robot Kingdom", there's a moment where it crosses this with Tear Jerkeras Doraemon and Maria are unable to escape from the rocket that is about to hit the moon, each of them gave Nobita, Poko and Jeanne their final words.
Maria: Jeanne, mom always believes in you.
Maria: Poko, please take care of your big sister, and no matter what, mom will always with both of you.
Doraemon: Nobita, please always do your homework, don't wake up late, try to not pick a fight with Gian and Suneo... and may you live happily ever after with Shizuka.
Even more heartwarming when the transporter device worked and rescued them.
In "Doraemon: Nobita and the New Steel Troops", when Pippo rants about how the Steel Troops would take over humanity, Nobita says that he doesn't want to fight Pippo. Cue Pippo breaking down in tears and walking up to Nobita, wanting to be held. By the next scene with them, Pippo is in Nobita's arms telling him that he doesn't want to fight either and wishes that Lilulu, who had been closing up to him recently, could have the same feelings.
Lilulu and Pippo's Character Development in general. Pippo learning about friendship from the gang and Lilulu getting her wounds treated by Shizuka cause them have second thoughts about their war against earthlings, and this leads to their Heroic Sacrifice in the end.
In "Doraemon: Nobita's Diary of the Creation of the Worldnote Nobita's Genesis Diary", the love confession and marriage proposal of Nobihide to Shizuyo (obvious expies of Nobita and Shizuka) is very sweet. Double so for the Nobi lineage to finally become successful like Nobita wanted.
In the movie "Nobita's Dinosaur 2006", Gian declaring he'll help while keeping Piisuke safe from the dinosaur poachers and get him back home at all costs, partially because Nobita saved his life from the Quetzalcoatlus earlier. He also (rather calmly) talks some sense into Suneo, who suggested giving Piisuke to the poachers in exchange of going back to their time.