What are some examples of research that does not solve a existing problem (maybe the problem is not obvious yet) but present a unique discovery?
Feynman noticing the periodicity of wobble and rotation of a dinner plate.  The fractional quantum Hall effect.  HTSC cuprates.  Initial discovery of superconductivity.  Michaelson Morely.  Many discoveries of new plants and animals.  Penicillin. Teflon.  The discovery of the Americas.