This probably started as a joke question for interviews, but it is also a fairly defining component of a photographer's style.
Some shoot very shallow all the time, others shoot with a great deal of depth. It can be the difference between being the selected photographer or not for some jobs.
Wide open with whatever lens I'm using. I'll stop down a little for focus or bright lights, but I generally prefer blurry backgrounds because it puts the focus where I want it.
I prefer f/11 or f/16 for landscapes (DOF and Sharpness).
Waterfalls about f/16 or f/22 (often with a 2 stop ND filter)
Macro- 5.6 or 8, sometimes wide open depending on what I am shooting.
I really like f 2.8 but f 4 is a good zone to be in for most of my outdoor shooting. It was fun shooting at 2.8 for the flowers I was into last week.
I'm now trying to find a shallow zone for food, that works artistically yet provides the right amount of info detail. Close up it's either f6 or f10. Betty Crocker shots from the 50's-60's f11 to f16.
The majority of what I like to shoot keeps me shooting between f/1.4 and f/4. I'm an existing-light kinda guy, I hate resorting to flash, and do so only when necessary.
I do like shooting landscapes, so occasionally do shoot at f/11 or f/16... except that night landscapes require f/4 or below, yet again!
With my Sigma (70-300mm) I tend to go as wide as I can so I can get a higher shutter speed.
1.8 with my 50mm. Of course I may reconsider this since I had so little DOF in my Battle of the Sexes entry. (And got marked accordingly).
Still learning where its better to have little DOF versus a lot. I guess when it comes to composition you have to think in terms of 3 dimensions not just two...