Aperture priority with Auto ISO for all my general photography. Shutter priority next and then full manual when I want to practice selecting more options. Only used full auto when I first got the camera just to learn some features. Tried P mode next, very briefly, but results were disappointing.
I used to live in aperture priority mode but that has changed. A lot depends on what camera I am using. When I use my low-light specialist, the Canon 6D, I sometimes shoot manual with auto ISO enabled, but with my Olympus OM-D E-M10 I can't do that because auto-ISO isn't available in M mode. Why? I have no idea. My Nikon D5100 lives in M mode because it's my uber-reliable 'round the house camera with an Eye-Fi card. Every picture I take has great color and great lighting with the bounced SB-24 I have permanently mounted on it. The lens is almost always the 35mm f1.8 and sharpness is just plain perfect every time. Oddly, I could find no mode selector on my new-to-me Nikkormat FT, so I think I shot manual.
I am usually too lazy to use full manual mode... I find myself in Aperture-Priority most of the time, but I'll switch to Shutter-Priority as needed if I know I need a particularly fast or slow shutter (think night photography or fast-moving subjects.) I'll do manual if I need to, but it's not that often. Auto-ISO, but I keep my eye on it. I set the base to 100 and I'll snap Auto-ISO off in my personal menu if it starts doing something wonky that I don't like.
I liked the comments of those who said they use "Professional Mode" and that they generally shoot in the "ON" mode. You guys are funny.