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In some simple cases such using the default Monkey as the object to project, the resulting cut looks nothing like the monkey. Note the selected cube only has only been cut around the monkey's eyes, not the entire object.
knife project with the default monkey
Trying with other primitives results in this error

No Other selected objects found to use for projection

I know that I have both objects selected.

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    $\begingroup$ Suzanne is non-manifold, so it just gets the eyes. Knife project is designed to work with flat 2D meshes as the projection object, so I think the overlapping faces confuses it. Collapsing a sphere into a flat circle and removing doubles makes it work as a projection object. $\endgroup$ – gandalf3 Sep 20 '14 at 0:01
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This is because knife project only uses wire or boundary edges:

Knife projection is a non-interactive tool where you can use objects to cookie-cut into the mesh rather than hand drawing the line.

This works by using the outlines of other selected objects in edit-mode to cut into the mesh, resulting geometry inside the cutters outline will be selected.

Outlines can be wire or boundary edges.

To use Knife Project, in 'object' mode select the "cutting object" first then shift select the "object to be cut". Now tab into edit mode and press "knife project".

emphasis mine

A boundary edge is an edge with nothing connected on one side, e.g.:

enter image description here

The primitives, being manifold objects, do not have wire or boundary edges.

Suzanne partially works because it is non-manifold (the eyes are disconnected). The two circles that you get by projecting Suzanne are the boundary edges around the eyes.

enter image description here

The error message is a little bit strange though.

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  • $\begingroup$ If Blender documentation could be as clear as your answer... $\endgroup$ – mins Jun 25 '18 at 18:27

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