Anywhere were two entirely independent entities share a one-to-one relationship. There must be lots of examples:
person <-> dentist (its 1:N, so its wrong!)
person <-> doctor (its 1:N, so it's also wrong!)
person <-> spouse (its 1:0|1, so its mostly wrong!)
EDIT: Yes, those were pretty bad examples, particularly if I was always looking for a 1:1, not a 0 or 1 on either side. I guess my brain was mis-firing :-)
So, I'll try again. It turns out, after a bit of thought, that the only way you can have two separate entities that must (as far as the software goes) be together all of the time is for them to exist together in higher categorization. Then, if and only if you fall into a lower decomposition, the things are and should be separate, but at the higher level they can't live without each other. Context, then is the key.
For a medical database you may want to store different information about specific regions of the body, keeping them as a separate entity. In that case, a patient has just one head, and they need to have it, or they are not a patient. (They also have one heart, and a number of other necessary single organs). If you're interested in tracking surgeries for example, then each region should be a unique separate entity.
In a production/inventory system, if you're tracking the assembly of vehicles, then you certainly want to watch the engine progress differently from the car body, yet there is a one to one relationship. A care must have an engine, and only one (or it wouldn't be a 'car' anymore). An engine belongs to only one car.
In each case you could produce the separate entities as one big record, but given the level of decomposition, that would be wrong. They are, in these specific contexts, truly independent entities, although they might not appear so at a higher level.
Paul.