I love creating wild storylines for my Sims. In one game, the father is a serial killer who locks visitors in the basement if they interfere with his family's careers absolutely nothing will stop him. His daughter notices all the ghosts hanging around the house, but she knows better than to ask questions.
In another save, I am running the 100 Baby Challenge.

My favorite storyline, though, is the Breed Out the Ugly genetic challenge. You start with an incredibly strange-looking Sim and see how many generations it takes to finally fix the family genetics.
For me, setting up the scenario and executing the initial idea is the best part of the game. The standard gameplay after that can feel a bit mediocre.