The most interesting thing I've seen done with 3D printing is definitely 3D printing of nano particles by a team at Harvard University to create very small batteries. The team aims to develop a method to 3D print entire electronics in a single output from one digital blueprint. They also aim to make the individual parts of the printer itself 3D printable, with the aim of making the 3D printing of these tiny batteries open source and accessible to the masses.

My dream 3D printer would include a self-replenishing filament system, in which used-filament material was automatically melted down, restrung and reloaded into the 3D printer. The printer would be a supportive element in 3D virtual reality experiences, such as those offered with Google Cardboard. Just as a video game preloads virtual game world elements into memory, this 3D printer would pre-print 3D tactile components into the space surrounding the VR user. These components would augment their virtual reality experience by providing real tactile elements to coincide with the audio visual components of their virtual reality. Just as the audio and visual elements of a virtual experience are allocated into CPU and GPU memory, the printer too would continuously recycle material and allocate the recycled filament to print new objects.