Kirk tries to save Spock, far too late to do anything to help him. Bones and Scotty tell him he can't enter the room, and that there is no hope.
They don't just tell him; McCoy knew how Kirk would react and was ready with himself, Scotty and a spare crewman to physically restrain Kirk from opening a door holding back unholy levels of radiation in his attempt to get to Spock.
McCoy: NO!, you'll flood the whole compartment!!
Kirk: He'll die!
Scotty: Sir, he's dead already!
Kirk calling for Spock, sobbing, even though they're Separated by the Wall. Spock, blind and dying, pulls himself up, straightens his jacket and painfully stumbles over to Kirk. Even at the last, Spock will never ignore his captain and his friend.
The eulogy deserves to be reproduced in full. Warning: will cause many Manly Tears.
"We are gathered here today to pay final respects to our honored dead. And yet it should be noted, in the midst of our sorrow, this death takes place in the shadow of new life, the sunrise of a new world; a world that our beloved comrade gave his life to protect and nourish. He did not feel this sacrifice a vain or empty one, and we will not debate his profound wisdom at these proceedings. Of my friend, I can only say this: of all the souls I have encountered in my travels, his was the most... human."
If you're trying to get through this scene with a dry eye, James Horner's soundtrack is not your friend. The end of the cue "Genesis Countdown" is Kirk's reaction to Spock's sacrifice. Unreleased on the soundtrack, but prominent in the movie, is Scotty on the bagpipes at Spock's funeral; his rendition of "Amazing Grace" swells into a full orchestra as the torpedo is fired toward the Genesis Planet, just as the sun rises over it. Cue Manly Tears, a lot of them.
The lingering shot of Spock's coffin as it comes to rest on the planet and pans out, showing the miracle the Genesis device has created ... and then Leonard Nimoy's voiceover reciting the famous Opening Monologue.
Spock: Space: the final frontier. These are the continuing voyages of the starship Enterprise. Her ongoing mission: To explore strange new worlds; to seek out new life forms and new civilizations; to boldly go where no man has gone before.
"...And also that I'm proud... very proud... to be your son."
The death of Peter Preston, Scotty's nephew, especially when he brings him to the bridge in his own arms. (Even Saavik sucks her breath in in shock.) Finally, Scotty tearfully states after Preston dies, "He stayed at his post... when the trainees ran."
Peter: Is the word given, Admiral?
Kirk: The word is given. Warp speed.
Peter: Aye... (dies)
In a scene deleted from the theatrical version, but put back in the Director's Cut, Scotty introduces the enthusiastic cadet to Kirk as "My sister's youngest, Admiral. Crazy to get to space!"
Combines a little with Fridge Horror when you stop and think about the Inferred Holocaust that goes along with Khan's attack; it hits hard to think how many of the trainees, even among those who ran, didn't make it out alive.
In the novelization, Saavik had been tutoring Peter Preston. The night before the funeral, she keeps a vigil over the coffins of both Preston and Spock, "the only two people she had ever cared about in the universe."