Yup, as Kelmo says, depends on the house, although all my houses were public for about the first 2 years I played. Certain incidents, mostly involving suspected exploits were what motivated me to make my main house with all my stuff private a bit over a year ago. Ironically though, I never lost a thing while my house was public, but my main house was looted just about dry (basically my soulstones, and Skylark's extensive wardrobe, which were in owner containers, were all that escaped) after it was made private, apparently by a friended char on an account which had been sold. But that is a different sort of security issue of course.
The Zento house was always meant as a service for players. It has always been public, although I did finally put security on the teleporters and lock the doors because it was a death trap, especially being so close to a public moongate. So, it never really accomplished what I wanted for it, but was OK.
Sometimes dealing with unwanted intruders on a non-combat character can be amusing, sometimes a royal pain.
I can deal with all public housing if that is what most people preferred. I can say definitively though, I would never want to return to a time when people could take over your house, with the whole key thing.
-Skylark