Passive Wisdom (perception) is common and we use it often. But I read on this forum that there are other passive stats. My Question is now what other passive stats exist and when should you use them?
Passive checks or scores are not limited in any way.
A passive check is a special kind of ability check that doesn't involve any die rolls. (PHB 175)
Is the only description we get, with the way to calculate them in the next paragraph.
In the absence of any limitations, all ability checks have a passive version technically, even though most of them are not used that way.
The PHB gives sparse guidance on usage, bringing up only two cases: average of a repeated task and for making the result of a check hidden from the players. This is vague. I use and recommend the following guidelines:
If there is a chance for success and failure, but no active effort is made and necessary, it is a passive check.
It takes no effort to look out of your skull, thus we use passive Perception. But if you start searching and look under boxes, you made an active effort at it and should roll a "normal" check. You don't have to crank-start your brain to reach conclusions, use passive Investigation. But you can cross-reference your notes in a library and that would call for a "normal" check.