Which 3D software should I learn for 3D printing?

[update] Added: FreeCad and Autodesk Fusion 360.
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At our MakerSpace, I am often asked for advice about what should someone use in order to create 3D objects for 3D printing.
There is not just one single answer because it depends on a few parameters so I made a little decision chart:
http://www.gliffy.com/go/publish/5271448

Please share your choices and advices in the comments.

The 3D files are there as exemples:

• The octopus is a Typical exemple of what you would use an the softwares on the left side for (organic shapes).here it was with Blender.
• The "central part" is a typical exemple of what you would use the softwares on the right for (precise dimensions). Here it was with Cubify Design

Disclaimer:
It is certainly not exhaustive or objective but it is based on quite a lot of reading, interviews and experiences.
This is a troll-friendly subject so please stay constructive in your suggestions to improve this decision tree.