Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
'"Elegy For A Pig" full stop. Malloy's emotion over his lost partner and the fact that his death seems meaningless and will be forgotten by most people soon.
The episode with two kids who are sent to L.A. by their mother who no longer wanted them and thought they'd get better care there. Just try not to tear up at the boy telling Malloy he doesn't want to grow up yet.
In one episode, a cop saves Malloy's life, but Malloy later learns that this cop is as twisty as a corkscrew. Malloy's shock and anger when the pedestal breaks are heartwrenching.
In one episode, a cop who had been hors de combat the previous eight years tries to catch up with changes in procedures, but is unable to in time to avoid spoiling several cases, and a near-tragedy ensues when they have to let a murderous stalker go as a result. He [the cop] is absolutely devastated.