CB Model Pro is an entry level surface modeler that's published by Dassault Systèmes, the creators of SolidWorks. You can use it to create all kinds of objects just by pushing and prodding objects in 3d space - much like working with virtual clay. You'll be using a basic tool set containing tools like Point Pull, Flatten, Bend, Neck, Scale and Poke. You can also draw in 2D on your models and then use these shapes for extruding or bending. Finally you can also 'paint' on your models using colors and decals.
It's a great tool for anyone who wants to get his feet wet in 3d design and it's great fun to play with. Having said that, it's unclear why the product is called 'PRO' because it's certainly lacking a number of pro-features (like having more control over your model and it's dimensions).
CB Model Pro is available for both Windows and Mac OS X, and it's completely free (although after 15 days you'll have to register for a free key to continue using it).
Due to the nature of this modeler, it's hard to create non-manifold objects, and it contains an STL exporter - the basic ingredients for having your model printed are both in place.
The exported STL files need a bit of cleaning up though - they trigger a 'non manifold' error after uploading to Shapeways (even though they're not!). This is easily solved though by downloading the open source package MeshLab, opening your STL with it and saving it as STL again. The default objects (cube, sphere etc) have a dimension of 1, so you should use 'inches' as the STL unit when uploading.
The website CB Model Pro Fans has published a number of nice video-tutorials and demonstrations that should get you started: