The short answer is it depends on the situation!
I use Manual exposure as much as possible when I'll have at least modest control over lighting conditions. This is now close to two-thirds of the time. I use a hand-held meter, almost always in incident mode to determine the ambient exposure, or in flash mode when I introduce lights.
In situations that happen too quickly for me to accurately respond, which includes much but not most of my action and sports work, I'll go into Shutter-Priority mode. I find the control dial very useful in adjusting exposure compensation quickly and many years of experience help me get it right - at least most of the time. Figure about 20-25% of my current exposures are taken this way, though this number was higher a few years back, before I returned to the habit of hand metering each situation.
For those times when I'm just walking around with my camera, when I'm playing tourist or have it with me for those "just in case" moments, I'm more likely to have it in Aperture-Priority mode. This probably happens about ten percent of the time.
I will almost never use any of the other modes, except Bulb for long exposures.
As for the other controls, I never use Auto ISO, while I'll almost always use Auto White Balance. My logic for this seeming contradiction is that I would rather chose how much degradation in IQ I'll find acceptable (and I can pretty quickly assess the general light level, hence ISO required for optimal results), but trust the camera more than my eyes for changes in color temperature. Amazing how quickly a cloud can pass in front of the sun. Since I shoot in RAW for (nearly) everything, I only need to be close. I can correct whatever errors in balance I've made in Lightroom and Photoshop.
