This idea was inspired by the rotating rings of the Game of Thrones intro. The rings are simply cylinders with the parameters set to give the desired geometry. I animated them rotating in different planes from 0 to 180 (half a full rotation), with sizes adjusted so that they don't intersect. Set the keyframe interpolation to Linear, and in the Dope Sheet (Shift F3) use the follow through to continue the animation in a loop (Functions: Track After: Continue After).
I love how well this turned out - it was just a playful project which rendered beautifully!