This completely depends on what I'm shooting and what I'd identify as the "subject".
For landscape and most architecture the entire "scene" is typically the "subject" and I want a broad DOF and I'll go out of my way to get it (even using tilt-shift to alter the plane of focus).
But if I'm shooting a specific subject where the "background" really isn't the "subject" then I tend to prefer a shallow DoF.
BTW, I don't do this to "hide the background"... I grew up with the notion drilled into me that every photo has a background and the background counts. So even though the background will be blurred, I'll still select a background that will look good when blurred.
I do not often go for an ultra-shallow DoF (e.g. I don't typically shoot at 2.0 or lower... even 2.8 is used sparingly. But f/4 is used heavily.) I don't want the DoF so shallow that I worry that my subject may not be within the DoF.
Also, choice of shallow DoF is typically for "one" subject shots. If there are multiple subjects (e.g. several people in a photo) then I avoid shallow DoF so I can make sure "everyone" is well-focused.