Especially on rescue missions. Two examples that come to mind are The Witcher 2 and Fallout 3 (spoilers ahead).
I’ve been playing the Witcher 2 and Saskia was just poisoned. So far Ive had a beer with the guys and banged an elf I saved in the first chapter; before even leaving Vergen’s walls. I chuckled at the thought of Philippa Eilhart asking what took me so long.
Fallout 3 is another prime example. Explaining to my dad that I was too busy being abducted by aliens and tracking down Nuka Cola Quantum for a museum to rescue him.
Are there any games where NPCs shame the player for taking on too many side quests?
I think in mass effect 2 the number of missions you do between personal quests affects the possible outcomes. Sometimes a character will send you a mail and be like: I just heard it’s too late, we didn’t get there in time.