Earth

Capitalize as the name of our planet.  Also capitalize Earthling, Earthlike. But do not capitalize "planet" in planet Earth. 

Do not capitalize earth when meaning dirt or the terrestrial part of our planet (compared with sea and sky) or in terms such as:

            earthquake

            earth-shattering

            earthbound (all uses)

            earthrise

            earthly

            heaven and earth

            earth sciences/scientist