What takes a mesh to have "Smooth Polygons" checked (Enabled), so it wouldn't puff out when rendered?

Could you rephrase your question? I believe you MAY be asking how to create a mesh that may be smoothed in the places where it should be smooth, yet not smoothed in the places it should not be smooth. I know my post will be followed by several going on about methods of splitting vertices. However, your phrasing "puff out" suggests STRONGLY to me you are speaking of a related -- Firefly-one -- behavior; where a cylinder will seem to inflate. Splitting vertices is not the solution to this particular problem. However, in my experience an additional edge loop will constrain the cylinder. I believe that only a cylinder with two edges shows this "bagpipe" property. In any case, adding another row of vertices (aka chopping the cylinder in half), fixes the problem.

When importing an Obj file (Mesh) into poser, then I do a render with "Smooth Polygons" enabled (by mistake). The mesh is buffy in image. So, when I uncheck "Smooth Polygons", the mesh in image is normal. So, what do I have to do when importing the mesh into poser, so I can have "Smooth polygons" enabled. And the mesh will not appear buffy in the rendered image.

Splitting vertices doesn`t always work, I have tried. :( What nomuse said will probably work, adding the row of vertices, there is no automatic way to make all meshes work with smooth polygons (meshes that have already been made earlier).

From your second post, it sounds like you are having generalized "marshmellow" effect. For that, either splitting, or adding micro-bevels, are the best methods. The "bagpipe" problem is peculiar to long thin objects built with single polygons down the long side. I like micro-bevels myself. But it depends on the mesh.

If you subdeivide the mesh, it should be high enough resolution not to look over inflated. Sounds like it is too low res to match the other items in your sceen. This way it won't be as puffy, but not faceted either.