Just after Robocop finds out Alex Murphy was KIA and goes to his former home to investigate. His house is up for sale but there are still some mementos that trigger his memories. Peter Weller's magnificent acting (when ONLY HIS MOUTH IS VISIBLE), conveying the realization of what Murphy has lost and how his life is changed forever should at least make you swallow hard. If it doesn't, you don't have a soul. And then as he storms through the house the music is a sorrowful rendition of "Rock Shop", AKA THE Robocop theme.
Just as Murphy is about to murder his own murderer in cold blood, Clarence manages to choke out "You're a cop...", and with the reminder of his duty literally flashing before his eyes, Murphy releases the brute and replies with grim pride;
Yes; I am a cop.
The New Years celebration in Robocop's first days of consciousness. There are some goofballs in this office.
While hiding out at the steel mill waiting for Boddicker to show up, Murphy tells Lewis she should get out of there. She replies, "Hey, we're partners".
After killing Clarence Boddicker, the first thing Robocop does before heading out is making sure Lewis is okay.
The Old Man: Nice shooting, son. What's your name? Not-"Robocop": Murphy.
He smiles at this point. He may be half-robot but he is still human.
While a crowning moment of funny on Robo's part, after saving the girl from being raped, the first thing she does is thank him and hug him, not even caring that the officer that saved her is part machine.
During the Unveiling, everyone's applauding Robocop on his first appearance. Morton himself is the top crowner of this as rather than make it all about him, he let's Robo know the applause is all for him.