Imperial Earth

Imperial Earth is a novel (subtitled "A Fantasy of Love and Discord") written by Arthur C. Clarke, and published in time for the U.S. bicentennial in 1976. It follows the protagonist (Duncan Makenzie) on a trip to Earth from his home on Titan, ostensibly to visit the U.S. for its 500th birthday, but really in order to have a clone of himself produced.

Warning: Wikipedia contains spoilers.

A number of other sub-plots suggest some sort of greater mystery, but remain unexplored. The book ends with him returning home with his new "child" (who is, without any surprise at all, female), leaving the other plot threads dangling.