In the episode "Dealer's Wild", the scene of Dr. Brackett telling the boy that his father had died would make anyone want to shed a tear or two.
In "Frequency," a friend of Johnny's is injured in a car crash and later dies on the operating table. Johnny volunteers to inform the wife that she's now a widow and does so in a very quiet, heart-wrenching scene.
Roy's distress in "The Virus" after Johnny collapses during a rescue and is brought to the hospital. You can feel the emotion when Roy is told his partner is out in the squad and he replies "temporary partner" because he is essentially emphasizing that he won't accept Gage dying.
The end of the "Greatest Rescues" movie. It's easy to get teary-eyed thinking of them having their own stations and not being partners, though it's obvious the friendship would continue.