Say you have a cube, and you remove one of the faces so that it becomes an open box. Is there a way to replace that face besides creating a new plane and manipulating it into place?

Extrude one of the edges.
I'm sure there's also a 'Fill hole' type of button, but I haven't used Max for modelling in a couple years and don't remember where precisely.

You can also create a new polygon (or do the same with two triangles).

Assuming this isn't what you meant when you mentioned creating a plane and manipulating it into place, if you edit the mesh and click "Faces" (for triangles) or "Polygons" (for a quad) in the Modify panel, you can then select a "Create" option further down. Then click on the vertices in either clockwise or counter-clockwise order. For a triangle, that means click three of the vertices and the triangle will appear (repeat for the second triangle). For a polygon, click all four vertices, then click on the first vertex again.

Your faces might not appear when you do this. If this happens, you've probably created the face so it is facing the wrong direction. Undo and click the vertices in the opposite order when creating the face.

Note: Some of my button names might be a bit off; I don't have Max in front of me at the moment.

If you convert your object to an EditPoly instead of an EditMesh object I believe that their is a cap or fill hole tool. Also, EditPoly is better if you plan on deleting edges while modeling because it maintains the adjacent faces if you use the Backspace key instead of the Delete key. Just a though.

Great, thanks; I found it under modifiers->mesh editing->cap holes.