I know what you’ve been thinking—why can’t 3D modeling be more like Minecraft? Well, the folks at 3D Slash have apparently been thinking the same thing. They’ve put together a web-based voxel editor that can export STL files for printing. The result should feel fairly natural to those with Minecraft experience.
Even though my quick little creation above is rather boxy, 3D Slash allows you to drill into each block, splitting them into sub-blocks upon sub-blocks. This allows you to model curves, defined in smaller and smaller pixels.
The editing experience is easy to grasp, though tool-changes can be unnecessarily slow (the switch between adding and breaking blocks is a great example, where you expect something simple like a shift-click to invert the action, but instead, you have click to a separate tool-selection screen every-time.)
Once you complete your designs, they can be easily exported as STL files for printing with your own printer, provided you register with the site.
[My Minecraft-inspired skeleton loaded into Repetier-Host, sliced with Slic3r.]
As an alternative experience for modeling, 3D Slash brings something fun to the table that is easy to start with. That experience counts for quite a lot when talking about modeling software!
[Edited 2014-04-29 with updated experience.]