Problem

Whole households are disappearing from my game. They are still shown as alive in the relationship panel but I can’t visit them or call them and their house is empty
My sim is gone. He’s not showing up in the portrait panel anymore.

Cause

There are different versions of this bug:

EA StoryProgression has moved the household away from your town. They are gone for good.
A Sim disappears after being taken in by the police.
Inactive babies and toddlers are being taken out of the world when the household they live in does not have the focus. They should get back into the game once you focus on that household or make it active though (although there might be sometime a problem with that, making those gone for good).
If left alone on a community lot, toddlers can disappear from an active household. They should get back as soon as an adult sim appears on the home lot.
Babysitters kidnap babies
After traveling, the baby / toddler that was left home, is gone.
Sim (especially ServiceNPCs) seem to exist in town but are never around.

Restore a backup
If your sim got taken by the police, he might be back in a couple days. Play on for awhile
Sim might be stuck somewhere, reset him

MasterController and Overwatch has an option to recover missing Sims (except when they have moved away)
StoryProgression has an option that can keep your sim from moving away
No Immigration or Emmigration for EA SP (registration required)