The definition of 3D in this thread varies a lot, mainly because none of these are "3D." What we're seeing is the perception of depth in a 2D image.
The things that contribute to this effect are, for the purposes of this thread, three things:
1) Separation from background and foreground into layers by way of DOF. The layers have noticable gaps between the level of focus they have. In other words, there's little graduation between major planes of focus.
2) It's further enhanced by contrast, or more accurately, "local contrast." That is, the contrast between two areas that lie next to each other in the photo. Higher local contrast "pops" the subject and lends to the 3D look.
3) Separation from the background by lighting, as in the dog picture posted. The light falling on the dog is brighter than the light falling on the background. It's another way of doing local contrast. Fill flash against a darker background is one way to do it.
Nothing complicated or mysterious here.. just basic photo principals that we all know coming together.
$.02