Personally, I like to shoot Aperture Priority about 85%, Program 10% and Shutter and Manual the remaining 5%.
I like Aperture Priority to control the depth of field; checking the shutter speed for hand hold ability and adjusting from there. I use program, typically at family functions, with flash, so I can hand off the camera to family/friends to take pics - without having to explain everything to them. Shutter and Manual, I use when I want full control over everything. As it is, I plan on shooting more in Manual mode, more to practice my technique than anything else. I tend to like my results with Aperture Priority.
Just as important, I think is metering mode, while I fully trust the metering in my F100, I'm still coming to grips with the D700, I like it a lot in Matrix, I am still trying to get better results with Spot Metering, I rarely use CW, though...not sure why.