Design-programs and tools I use / have tried

Blender

Versatile program to create objects, graphics (rendered images of 3D scenes) and animations. Not easy to learn, but very powerful. Example: Vikings logo 3D

OpenSCAD

Create objects with scripts. Variables, functions and modules make exact control over objects possible. Well suited for technical designs, not for organic structures. Example: Heightmap puzzle

Inkscape

with Inkscape to OpenSCAD converter

Inscape is a program to create SVG-graphics. With the plugin complex shapes can be exported to OpenSCAD and processed further there. Example: rune stones

TinkerCAD

Easy to learn CAD-program. Basic-shapes are arranged, combined and blended.

Meshmixer

Easy to use. Basic-shapes are arranged, combined, blended and treated like virtual clay. Well suited for organic designs. Example: German Shepherd bust

Sculptris

Sculpt with virtual clay.

3D-Builder

Repair objects automatically.

Repetier with Slicer

To slice and print. Even if you don't print yourself, it's good to check the printability of your design.