You need to assign smoothing groups to get the polygons to render without facets.
select the polygons you want to be part of one smooth group then in your editable polygon menu go to the polygon properties rollout and assign a smoothing group.
Smoothing groups allow you to create sharp edges between smooth areas like between the caps and surface of a cylinder. If you assigned one smoothing group to the whole cylinder you'd get a sort of capsule. Smoothing in this sense is a way of shading the polygons to "appear" smooth rather than actually adding more polygons as with the turbosmooth modifier. You can also use the "smooth" modifier to assign smoothing to an object or sub object.
Adding a turbosmooth modifier will smooth out your object but it will also change the shape alot. you have to add extra edges to the mesh to define hard edges after smoothing. (Look at sub-division surface modelling.)

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Dear Tyson! Thank you for your thorough answer!
Have a nice day!

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One more question. If I plan to use my model, made in 3dmax, in a game. Well then I guess, I'd better not use this smoothing method, since this "smoothing group" information only means something for Max. Instead, I should refine a model by modifiers like Turbo smooth etc. Right?

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As far as I know, it depends on the game engine. Some will retain that sort of information, others won't.

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