"Of all the souls I have encountered in my travels... His was the most... human." Doubles as an EPIC Tear Jerker.
"You are my superior officer. You are also my friend. I have been and always shall be yours." It has a heartbreaking callback later, but the initial moment warms the heart indeed. Perhaps even more heartwarming in the way Spock says it - a simple, matter-of-fact utterance, as though it's an essential, inevitable and natural part of who he is. He could have been reeling off "Spock, son of Sarek and Amanda, Science Officer and First Officer of the Starship Enterprise, friend to Captain James T. Kirk..." And considering Spock's personality, for him to matter-of-factly accept any emotion whatsoever...! Yeah. Whatever the nature of their relationship was, those two men loved each other.
"I have always been, and always shall be, your friend. Live long... and prosper."
The reconciliation scene between Kirk and his son - "I'm proud....very proud..to be your son."
Because the needs of the many outweighed the needs of the few.
"I feel... young." The whole theme of new life and new beginnings, even after death and tragedy, is truly heartwarming.
Over the course of the TV series and films we've seen Spock and Bones argue about just about anything but in this film they are both in total agreement, albeit in different scenes, that Jim accepting promotion was a huge mistake on his part and they urge him to get back his command. It's nice to see them finally agree on something.