Any respectable modern camera should have Tv (shutter speed priority), Av (aperture priority), and M (manual control) modes. I use M and Tv modes almost exclusively. I use M and Tv modes to control my aperture. I can't remember using Auto or Program or Av mode this year.
In Tv mode, I increase shutter speed to automatically decrease the DOF (depth of field), and decrease the shutter speed to increase the DOF.
In M mode, I generally want to lock in my shutter speed based on the subject, and the lens used. When I make pictures with my hyperactive kid, for example, my camera settings are, 50 mm focal length, 1/500 shutter, iso 400. I manually adjust the aperture to get a properly exposed picture.
Is there ever a need for Aperture priority while hand holding a camera? Not really. Since I never want to go below 1/(focal length) for shutter speed.
Depth of Field in Portraiture
There are some factors that drive my decisions on what aperture to use in different situations. If I am doing a portrait of a person with a cool building in the background, I'm going to use a small aperture to create a high amount of focus depth to get everything sharp in the shot.
If I want background blur on the portrait or just instantly blur out unwanted features such as ears, I'd use a larger aperture to limit my depth of field.
When controlling depth of field, there are no magical f/number (aperture) on all lenses of all cameras. A source of confusion can be found here
http://youtu.be/oobLnqpuAk4. Depth of field changes due to several factors, sensor/film size, focal length, subject distance and aperture.
How far away are you standing from the subject? What format (6x6, 645, 35, APS, micro 4/3, compact...)? How tight are you framing?
Assuming you like taking portraits at 6 ft with 35 mm format, 85 mm lens at f/5.6 which give you over 5 inches depth of field.
I shoot 645 format so, 150 mm lens at f/11 gets me a little over 5 inches depth of field 6 ft away from subject.
On a Canon S95, 22.5 mm focal length, 4 ft from subject gives you about the same 5 inches depth of field. the framing is tighter, but workable.
If 6 inches depth of field is what you think is the best for portraiture, that's cool.
I'm just throwing this in here since there are a lot of amateur format shooters out there that would get everything in focus all the time and can't seem to create what they want.