Aulë's creation of the Dwarves. Impatient that no mortals have yet awakened, he makes his own race, and makes them tough and resilient, knowing Morgoth's power is out there and must be resisted. Eru Ilúvatar then intervenes and points out that, because only he can give the "Secret Fire" of true life, all Aulë has achieved is the same thing Morgoth and Sauron can do - not to make, but only to mock, and the dwarves are just mindless golems doing Aulë's will. Aulë repents and tearfully takes up his hammer to destroy the dwarves...only for them to cower in fear, something that did not come from Aulë's mind, and Eru reveals he took pity on him, as his intentions were good, and by his grace has given the Secret Fire to them so they might live.
Especially touching was Aulë's reaction when Eru calls him out on creating the dwarves: he emphasizes that he meant no disrespect like Morgoth, and compares himself to a child mimicking the actions of his father; not from mockery, but from a love and respect for his father.
Worth noting here is the fact that while Dwarves are certainly not portrayed in the best light, most being self-interested neutral types, they are by far the most difficult race for the Dark Powers to corrupt or trick. In fact, of the seven Dwarven kings who are given rings of power by Sauron, only two join him, another three stay out of it, and two are actually helping the Last Alliance, DESPITE the rings having been in their possession for centuries.
Similarly, Eru taking pity of Yavanna and making the Ents to ensure her plants at least have a line of defense.
Fingon rescuing Maedhros, despite believing that Maedhros had betrayed him.
Elu Thingol's first meeting with Melian. Also, when Morwen begs him to shelter her son and, in response, he picks little Túrin up and sets him on his knee, unexpectedly taking him as a foster-son.
Eärendil is not only spared by the Valar, despite breaking a couple pretty big cosmic rules by stepping foot in the Undying Lands, but they grant his prayers to save what is left of the Elves and good men in Beleriand because they are touched by just how deeply he cares for both kindreds (and this DESPITE the fact that the sons of Fëanor had just kidnapped his sons and tried to kill his wife).
The whole situation is also one for Ulmo, who introduced the loophole into the protections around the Undying Lands that the greatest of mariners could pass through them, knowing full well that one day someone would care enough to come beg the Valar for help.
Maglor fostering Elrond and Elros. "...and love grew after between them, as little might be thought."
The tale of Beren and Lúthien Tinúviel, a mortal man and an Elven princess fall in love. Lúthien's father sending Beren on an impossible quest, while imprisoning her couldn't keep them apart. Sauron imprisoning Beren couldn't keep them apart. Not even death itself could part them from each other! Interestingly, Lúthien was created in homage to Tolkien's wife, Edith Tolkien, while Beren was basically an Author Avatar. Edith was dark haired like Lúthien, while the elf's sacrifice of love was paralleled by Edith becoming a Catholic for Tolkien at the cost of estranging herself from her birth family. Tolkien even put "Beren" and "Luthien" on his and Edith's gravestones.
In short, the fairest Elf to have ever lived and the most beautiful story in Tolkien's entire mythos was inspired by his wife.
In the bad guys's side, the Balrogs rescuing Melkor from Ungoliant. Granted, given it's the story of Arda what we are referring, you will be hard pressed to feel any sympathy for Morgoth and his demons, but it is still heartwarming to see that even the most miserable beings in the Middle Earth aren't devoid of things like loyalty and friendship. They could have left Melkor to be devoured and would have got away with it, but even so, the Balrogs chose to come to his aid not caring they would have to face an creature whose darkness was even mightier than theirs and who was feared by the Valar themselves. But not just that, they actually defeated her and drive her away from the known world. It is not there in the text, but you know Melkor afterwards felt so proud of them.