IMO, there is no certain age at which boys and girls should not play together.  Of greater concern is the kind of "play" and availability of direct adult supervision.  Obviously, 13 year olds of mixed gender ought not be playing together unsupervised or at all at, say, a physical sport like basketball.  On the other hand, may they hike up a mountain with their families present?  I see no reason to prohibit it, so long as there is a responsible adult and they aren't allowed to go off together alone, or to hold private conversations.  My family used to camp with a non-related family whose son was my age.  When I think back on it, Don and I were never "alone together," not even in the company of our younger siblings.  We are both oldest children.  
In my first-grade classroom, I arrange separate play groups for boys and girls at their recess.  Both may play at the Lego table, but not at the same time.  Even at the tender ages of 5, 6, or 7, bad things can happen.  Use an ounce of prevention and save yourself a pound of trouble.  In so doing, you may well be saving a child's soul, and your own.