Since early spring I've been hunting conic sections in the wild. Let me start with some examples and not bore you with the mathematics:
There are many - more complex - situations that produce conic sections. Marcel Minnaert describes one of them - the interference pattern between vertical fence-posts and their shadows. Actually - I seemed to remember that Minnaert had proven these to be hyperbolas - but when I searched his writings I didn't find the proof.
How often do these conic sections occur in nature? One simple experiment is to count their occurrence in the works of Marcel Minnaert, on Flickr and on Google picture search. This yields the following results:
Conic sections - Wikipedia