Where can I get a program, preferably free, that can translate mesh objects from .3DM and/or .MAX formats to .OBJ or .3DS or .DXF format?

You can do it INSIDE Max with HabWare's Max2obj (and obj2max for the other way around)

Does that mean that I must buy Max first? If so, who sells Max and at what price?

Ah sorry. I assumed that since you had Max files you had max as well. My bad. I've never heard of any program apart from Max that reads Max files.

Attached Link: http://www.righthemisphere.com/products/dexp/index.htm

Deep Exploration is supposed to be able to convert MAX files, but most of the time I got strange results. I too have heard that MAX format is pretty special hence there isn't really any converter for it. Pitty, cause there are so many wonderful free models out there in MAX format... Oh and Deep Exploration is a bit costly too... 3ds Max is from Discreet products and is pretty pricy too: http://www.discreet.com/products/3dsmax/

The way i understand it, a .MAX file is a 3DS Max scene file; while a .3ds file is just one model. I also understand that Deep Exploration won't convert .MAX files unless the user has 3ds Max installed. I could be wrong, though.

Max is about $3500 - but I was amazed when I looked at taking some 3D courses at my local university that they could sell the educational version of Max for $360 + $300 for the course.

Nothing but max will open a max file (properly I should say). A max file is the scene( cameras,lights,plugin info sometimes, and the objects. A 3ds file can be more than one object as long as the face count is under 64k. I never messed with 3dm format so I can't help there.

Your best bet is to get the author of the MAX file to convert it for you; most of them will. I think I read somewhere that Polytrans can do something with them, but i'm not sure.

Correct, 3Dexploration Tries, but fails most of the times to convert .MAX files. But, notheless it's still one of the best & most complete 3D converter out there. The .MAX format is written in such a way that it's Native to Max. Most of the Big Modelers are the same. Since they all manage Geometry, Mats, Lights differently, it's almost impossible to interchange them... Best example is the "Modifier Stack" in Max. Or the "Nodes" method in Maya... They each have their Strengths & weaknesses... Those will be enough to make it hard to extract just the mesh out of them without losing info. As RealDeal said, best to ask the Author of the Mesh Directly. I have Max, cuase i teach it. So the school bought me a version for home, so i could do most of my work in my Pijamas. :-) 3dm?? Rhino file? Marco