There are rational reasons for having children, and there are irrational ones. As long as humans have existed, people have propogates for both kinds of reasons. No, you don't have any responsibility (i.e., "duty") to your ancestors (or even your parents); the rational thing to do is to act in your own self-interest (but not at the expense of others, which is actually subsumed by acting in your own self-interest).
Objectivists should be concerned about the future of the race and planet, only to the degree that it's in one's rational self-interest to do so. So, for example, I'm not worried about recycling or using "green" energy, because I don't believe it's in my self-interest to be concerned with those kinds of things.
Further references: I would highly recommend that you obtain the book "The Virtue of Selfishness," which presents the Objectivist ethics. Another good thing to read, if you have not done so already, is Atlas Shrugged.
Jan 26 '11 at 00:36