You can use any of the 3D Modeling softwares, as long as you follow the basic design guidelines given above and export the output as .stl file.
A list of some of the softwares that you can use for Designing your 3D Model
Free 3D Design Softwares
Google Sketchup: Easy to learn, create and export your 3D Models. SketchUp Make is a free version and SketchUp Pro is a paid version with additional functionality. Works in Windows and Mac
Tinker Cad: Simple Browser based Software that can help you create complex stuff using very simple tools.
Blender: A free, powerful open source 3D content creation suite, available for all major operating systems under the GNU General Public License. Works in Windows, Linux and Mac
OpenScad: A free software for programmers for creating Solid 3D CAD objects. Works in Windows, Linux and Mac.
Netfabb Studio Basic: Free software for STL file slicing, repair. Works in Windows, Linux, Mac. Netfabb also provides a free cloud based mesh repair module.
123D Design: A powerful suite of Apps/ tools from Autodesk. You can create a 3D model from scratch or pick a 3D model from the library and customize it to your liking. Works in Windows, Mac and browser.
Free CAD: An open source parametric 3D modeling software that allows easy parametric editing of your design. Works in Windows, Linux and Mac
Sculptris: A free digital sculpting tool ideal for starters in digital sculpting from Pixologic, the makers of ZBrush. Works in Windows and Mac
3D Tin: A Browser based program using WebGL.
Commercial 3D Design Softwares
Rhino: A Popular 3D modeling software based on curves, using NURBS mathematical modeling. Works in Windows and Mac.
Maya: High end 3D modeling tool to create complex models and has additional functionalities like rigging, dynamics and animation. Works in Windows and Mac.
Solidworks: An advanced 3d modeling software, suitable for mechanical, industrial product design that require high precision. Works in Windows and Mac.
3DS Max: A comprehensive 3D modeling, animation, simulation, and rendering software. Works in Windows.
Autocad: Great CAD design and documentation tool, ideal for architects, engineers and product designers. Works in Windows and Mac.
ZBrush: A digital sculpting and painting program with powerful features and intuitive workflows. Works in Windows and Mac.
Netfabb Professional: an advanced software for professional editing of 3D printing data. Helps in fixing 3D models and reduce risk of failed builds and wasted material. Works in Windows, Linux and Mac.
Mudbox: A popular digital sculpting and digital painting software from Autodesk. Works in Windows, Linux and Mac.