When / Why do you show your cards when folding?

I have auto-muck set and I always thought showing my cards is just giving away information I don't have to. Clearly, this is not the whole truth, and I'm thinking of turning off the auto-muck and showing sometimes. But when?

This is all prompted by a recent post:

Originally Posted by OngBonga

I fold and show so he thinks this is a good way to bluff me and a bad way to get value from me. Wouldn't make the same fold next time.

What considerations do you make when showing a fold?
Are they different reasons than showing when you WWS?
How should I approach this?