EEM London's "Case of the Blitz Beryls," especially when you're told the history behind the titular beryls and the fact that Roscoe Fishwick has a dead little sister who was killed during World War II.
Jake/Jennifer: We're very sorry that Fiona died, Mr. Fishwick.
Mr. Fishwick: It was many years ago, but I still remember her and miss her.
In the same game's "Case of Macavity's Mace," the protagonists learn from Lady Edna Saltcoats' Girl Friday, Julia Beeswing, that Lady Edna used to have a pet monkey who died after being caught in a rabbit trap. Later, when your partner tries to bring it up directly to Lady Edna, this is the response (and Lady Edna's voice actress is very convincing):
Lady Edna: I'm sorry, but I won't discuss it with anyone, ever.