What mode is your camera most often in? Why?

I am no artist - take images mostly for pleasure. I am doing it for quite a long time and went far beyond family album photos - but have not ever sold an image. The question you are asking has only one correct answer - it depends. It depends on camera and on the subject of your photograph. For example, if you are taking photos with a compact - fully manual controls may be not available at all. If you are taking photos of  sporting events - thinking and fiddling over manual settings may rob you of some interesting frames.

Yes, many people take images in aperture priority mode - it gives the photographer incredible flexibility with depth of focus and exposure control. And it's still semi-automatic - as camera chooses the shutter speed. Here might be a trap, as the exposure may get too long for taking a sharp image handheld. This mode needs considerable experience and skill to use.

For myself, when I go out with a "serious" DSLR camera, Program shift mode "P" is a favorite one. I set the ISO, and then shift the aperture/shutter pair whatever way I wish - leaving it to the camera to adjust to light changes. This mode is very flexible - when taking images of fast moving objects I move the pair to shorter exposures/open aperture, when taking landscapes - to longer exposures/tighter apertures. And, when I am simply after happy holiday snaps with my pocket camera, may simply leave it in full auto - cause I share the camera with my wife and oftentimes ask my friends and friendly strangers to push the button for a whole family photo