As a submariner, I have been brainwashed into having a very critical attitude towards maintenance, inspections and monitoring.
I'm constantly checking rigging, lifelines, hull penetrations (shaft, seacocks, through-hulls). The slightest amount of water in the bilge makes me grind my teeth.
I watch my engine gauges like a hawk when motoring. I check the bilge regularly while cruising. I listen for any cycling of the bilge pump and the shower sump.
I'm nervous when I set out for the first sail of the season. I begin to relax after making rounds of the boat and finding everything working properly.
I'm nervous when darkness falls. I usually relax about 30 min. to an hour after full darkness when I realize that the keel isn't just going to fall off because the sun set.
I'm nervous for an hour or two when I cross the boundary into the Atlantic. I manage to relax once I convince myself that the mast could just as easily fall down while inside the Chesapeake.
Capecodda is right about prioritizing. I also have that mindset. I think I'll call it "Capecodda's hierarchy of needs."
Anyway, a total lack of fear keeps you ignorant to your environment and will lead to complacency and eventually, some sort of casualty.
Too much fear can be just as detrimental. It can force you to freeze during a critical moment or affect your judgement in other, negative ways, not to mention sucking the joy out of sailing.
The right amount of fear (or caution, if you prefer) keeps you aware of what's going on around you, causes you to be introspective and think about your actions and decisions but still allows you to function at a high level.