The end of manga volume six and beginning of volume seven, which deals with Doraemon returning to the future (because the authors thought the series wasn't as successful as they thought it should have been and cancelled it) and coming back (when it turned out that it was as successful as they thought it should be).
In the episode "Two Shizukas", Nobita is stuck at identifying which is the real Shizuka 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*
In Doraemon: 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 and the Robot Kingdom crosses this with Tear Jerkeras Doraemon and Maria unable to escape from the rocket that's 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 heart warming 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 Riruru, who had been closing up to him recently, could have the same feelings.
In Nobita's Genesis Diary, the love confession and marriage proposal of Nobihide to Shizuyo (obviously an expy of Nobita and Shizuka) is very sweet. Double so for the Nobi lineage to finally become successful like Nobita wanted.
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. 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," making the young cat-robot cheer. 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.