37 weeks

How your baby's growing:

Your baby is now considered "full term," even though your due date is three weeks away. If you go into labor now, his lungs will likely be mature enough to fully adjust to life outside the womb. (Some babies need a bit more time, though.
Your baby weighs 6 1/3 pounds and measures a bit over 19 inches, head to heel (like a stalk of Swiss chard). Many babies have a full head of hair at birth, with locks from 1/2 inch to 1 1/2 inches long.

 Here is something interesting that I read in an email from Research Medical (where I am delivering):

What is a “due date,” anyway?
While your due date may still be a couple of weeks away, as of week 38 your baby is considered full-term. While we often focus on a single day—as if a delivery before that day were “early” and one after is “late”—the truth is that your baby is due anytime between weeks 38 and 42, and your due date is simply the day that falls in the middle of that period.

So then why are we so quick to induce women the week of their due date?  (sigh)  
Baby Smith can take as long as she wants :)