And now for the modeler on a budget:

MilkShape 3D

Originally designed as a low-polygon modeler for the computer game Half-Life, MilkShape has expanded over the years to support numerous games and file types. It includes basic tools like subdivision, extrusion, weld and unweld, etc.

I've used MilkShape to create all of my contributions to Free Stuff.

Strengths:

Clean, simple interface
Expandable through third-party plugins (SDK readily available)
Updated regularly (every few weeks, on average)
Supports dozens of 3D file formats
Excellent mesh-smoothing and mesh-reduction tools
Inexpensive ($25)

Weaknesses:

Polygons only (no nurbs, splines, patches, or whatever you call them)
Triangles only (quads aren't supported)
Polycount limit (16384 triangles maximum)
Limited UV-mapping tools