I have been on the receiving end of this behaviour several times.
1st time at 15 or 16, dad went through my emails. I was only a slightly moody teen, and maintain there was nothing in my behavior to suggest that they had cause for concern. There was an email read from a friend who was going through an extremely rough patch and had trusted me with secrets.
2nd time as a legal adult but still living at home, mother went through my phone, there were flirty but not outright sexual messages between myself and a male friend. Friend, not vague acquaintence. She still berates me to this day over "sexting"
3rd time my sister had broken up with her partner and moved on in a short space of time. I was staying at her place with her, left phone out, her unpleasant ex let himself in with his old keys, proceded to read all the texts between sister and I. Mother was outraged at this invasion of privacy (see above point and amuse yourself with the hypocrisy).
I say it is never appropriate unless someone says "here is my password, feel free to read everything". Or someone has disappeared, I guess it's ok for police to check these things if it might save a life :) Actually, if someone's computer has been connected with nasty things like child pornography, I say it is highly appropriate for professionals to access their information and get the fucker locked away.
But on a day to day basis, I think it is highly inappropriate.
Sorry, can't get tags to work.