3D modeling software seems to take one of two perspectives: Artistic or Engineering.
Artistically oriented
Blender
The open source gem of the 3D modeling world. Primarily aimed at 3D visual modeling and animation, it can also be used to prepare 3D printable models. Making 3D-Print-ready STL files requires some care. Enormously rich and complex user interface, but much can be ignored (shading, animation, etc), if you’re only interested in creating printable models. Tons of info online.
MoI
Moment of Inspiration is a relatively inexpensive 3d modeler that runs on PC, Mac, and Linux. Less full featured than Blender or Inventor, this makes it a lot easier to learn. It produces great STL files as long as you are careful that your exported objects are solids (see FAQ about manifold).
Engineering oriented
OpenSCAD
OpenSCAD implements a programming language for 3D modeling. There’s little it can’t do, but you really have to be a computer programming nerd to use it. If that’s you, have a look; you might like it.
SketchUp
Formerly ‘Google SketchUp’, the 3D modeling tool has been around a few years and has developed a strong following. You must install a plugin to export STL files. Be careful: the exported STL files can have flaws that must be cleaned up prior to slicing.
FreeCAD
FreeCad is an solid modeling CAD program with a modeling paradigm much like Autodesk Inventor or Solidworks. It’s pre-beta and has bugs and incomplete documentation, though a quick web search usually finds anything). Nonetheless, it’s quite capable. Your author is a big fan and has never seen it produce a flawed STL file.
Solidworks
A very popular, professional 3D modeling tool. Very expensive.
Autodesk Inventor
http://www.autodesk.com/products/inventor/overview
Autodesk’s answer to Solidworks. Also very expensive.
Autodesk Fusion 360
http://www.autodesk.com/products/fusion-360/overview
Autodesk’s cloud-based modeling tool. Very capable and free for hobby use. We used to frequently host classes on Fusion 360, taught by Autodesk’s own instructors.