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I haven't done any case studies on the matter or scientific mumbo jumbo, but to me, on 3-D-ness, it's pretty easy.
1) You need an appropriate subject, subject-to-camera distance, etc. I believe the whole 3-D aspect of an image is because it roughly estimates what our eyes and brain would 'render' were we that close (or far away) from the scene.
2) The proper amount of background blur. Too much and it's going to look fake, look digital, look like something we wouldn't see. Not enough, and you're not going to get a good sense of depth. Plus, it's got to be good blur - lots of rough bokeh edges, cat eye effects, etc. are going to jar the viewer and remind them it's not real.
3) Micro-contrast - specifically, good contrast (including edge contrast) in the subject, because our eyes naturally see more detail and contrast up close than far away. This is also going to help separate the foreground objects from things behind it.
4) The right photo to begin with - some just work more than others. For instance, I've not yet ever seen a strongly backlit 3-D looking photo. Most everything that I see as 3-Dy is side-lit or with diffused light.