Used to live in the LA area. A while back, I remember hearing that KS’ nickname on a movie set (sorry, I cannot remember which movie) was ‘Nut Palmer’. I don’t believe he has ever married, and he seems to keep a low profile about his personal life.
http://gawker.com/remember-when-kevin-spacey-groped-a-male-model-in-publi-1663777132