"Neo, I'm not afraid anymore. The Oracle told me that I would fall in love and that that man... the man that I loved would be The One. So you see, you can't be dead. You can't be... because I love you. You hear me? I love you. [Trinity kisses Neo; Neo's vital signs return] Now get up!"
Though heartwarming may not be the right word for it, Agent Smith's speech to Morpheus in the first movie implies not that he is some G-man working for a higher power with no real feelings of his own, but rather a sentient intelligence whose only real desire is to be free from what he perceives as a prison. Buried in a speech about how much he hates humanity is a hint that he may be more human than he realizes.
The scene in Reloaded when The Kid hands Neo a gift from one of the orphans, saying he would understand. It is a spoon. Neo smiles in relief, as it means that Spoon Boy was freed from the Matrix.
All the scenes with the girl Sati in Revolutions count, despite the fact that she's not even human.
During his meeting with the Architect, the screens surrounding them show different choices Neo might make throughout the scene. When the time comes between going to the Source (saving humanity from extinction) and returning to the Matrix, there isn't a single scenario where he chooses anything other than saving Trinity's life.
Toward the end of Revolutions, Neo escapes the Sentinels by pushing the Logos as fast as it can go...and it goes above the cloud cover. Trinity becomes the first Human in untold centuries to see what's above the clouds: the bright, unspoiled blue sky and warm yellow Sun. It's one of the last things she sees before she dies. An image of beauty to take with her to the next world.
A Detective Story: The scene when Ash's cat throws him his hat. At the end, when the mortally wounded Ash offers to stay behind and buy Trinity time to escape the Agents, she gives him the highest compliment a Rebel could ever give a Bluepill, "There's a difference between a test and a choice. For what it's worth, I think you could have handled the truth."