In this video 3D Printing Systems shows a model they make of an impossible object using a Fused Deposition Modelling machine. Fused Deposition Modelling (FDM) is an additive manufacturing method (ie. a type of 3D printing) where a filament of material is heated and extruded to build layers of the model which fuses as it cools forming a solid model. The printed material could be a thermoplastic or a metal.
In this video the 3D printed object is essentially a series of nested full complement ball bearings. The outer race of each bearing is mounted in a gimbal like manner to the inner race of the next largest bearing to create an object that would be difficult to create by other methods of manufacture. Whilst this 3D printed part may not be particularly useful, the model created shows the power of 3D printing and it’s ability to produce a complex component made up of multiple parts in a single print.
You could also use 3D printing to do the opposite and make one single part that would normally take multiple parts and processes to make simplifying the manufacturing process or optimising the design.