My parents are very honest people.  But I have my mother's discomfort with confrontation and my father's obsessive thinking and difficulty with decisions.  My father's decisiveness was a reaction to his father's extreme indecisiveness when they were both dealing with the same decision-making anxieties.  But I got in the habit of lying about things great and small to deal with my problems with communication and trust.  

I have no idea how to influence my kids to be honest.  I don't even know if I can be a role model that way, although I know I need to.  And even that might not be enough.