One of the coolest little objects we've printed so far is this model of the Borromean rings. The Borromean rings consist of three rings that are configured in such a way that all together, the three are linked -- but no two of the rings are linked to each other. This means that you can't unlink or separate the three-ring object, but if you were to remove any of the rings the other two would just fall apart.
An interesting fact about the Borromean rings is that they can't be made with circles. In the picture above the rings are in fact ovals; if they were circles then they would not be able to be arranged in the Borromean configuration. The cool thing is, the student who was making this model with Tinkercad discovered that first-hand, before she knew that fact. This model was printed on a Replicator 2 with a thin, removable support structure (using the default raft and support Skeinforge settings) that kept the rings separate during the printing process. The model moves freely and can squash down like this:
In the squashed configuration you can start to see that this is actually a three-component spiral link with three strands, three repeats, and an "under-over" pattern, that is, the spiral link known as S(3,3,(-1,1)). More on this later.