Well, I can't recall anybody ever implying that the world was necessarily a 'safe' place ...
However, while Prudence and Paranoia may both start with the letter 'P', I can't think of much else they have in common.
http://www.m-w.com/dictionary/prudence
http://www.m-w.com/dictionary/paranoia
The possibility of coming home to an intruder ...
Just my thoughts ... but while being surprised after having already entered a home without any indication of an intruder being present is one thing, having some advance indication before entering may be something else ...
FWIW, I've received some degree of training when it comes to searching and clearing residential/commercial structures and properties. I get frequent opportunities to practice these skills in the course of my LE duties, too.
At work I have additional resources available on a daily basis for such situations ... in the form of a partner, additional units (plainclothes & uniformed), K-9's and even mutual aid (should it merit more resources than available in any one agency at any particular time). Like many cops, I've been called to assist outside agencies in such circumstances, too.
I generally have more equipment available during working hours, too.
Naturally, like most other folks who think of such things, I've considered my reaction to returning home and finding indications of my home having been forcibly entered.
Unless I heard my wife inside calling for help, or had reason to believe she was actually inside and in immediate need of help, I'd call in the local agency and let them do their thing. They have resources similar to mine when I'm working, none of which I have at hand when I arrive home, in another jurisdiction.
Since the question was just
Do you carry every time you go out?, I'll skip the what-if's of remaining home ...
Since I'm not
required to remain armed off-duty, however, and there are still situations and circumstances in which I feel I do not feel it necessary, appropriate or simply desirable to be armed on my own time ... there are times when I choose not to go out armed.
This doesn't mean my usual awareness is in any way degraded or lessened, however, or that my ability to react strategically or tactically is completely neutered.