Q:

Seeing the shadow of a black hole

Why can't we see the shadow of a black hole cast on Earth. Shouldn't the black hole block some light from a star or a galaxy far behind as they line up?

A:

Yes, it will block some light. But barely anyone would notice if Gliese 581 were suddenly covered up by a black hole, and it's only 20 light-years away. The closest known black hole is 1600 light years away. You'd need some pretty sharp vision.
Also, you're going on the assumption that black holes block light like normal objects, which they don't. They do it like this: https://en.wikipedia.org/wiki/Gravitational_lens#mediaviewer/File:Black_hole_lensing_web.gif
Black holes are weird :)

