I'm 38 weeks pregnant and I'm SO ready to see my little boy. At my 37 week checkup he wasn't even engaged in my pelvis yet though. :(
I've been doing certain things to sort of "move things along" as you will. My opinion of natural induction techniques is that they won't work unless your body is ready to have the baby anyway, so there's no real harm in trying. (Just don't expect a ton of results.)
That said, there's no real way to single-handedly prove my theory, I've just come to that conclusion based on a bazillion testimonies from other women (mostly via internet forums but some I've actually known in real life.) :P I didn't have a cervical check at 37 weeks, but at 36 weeks I was slightly effaced (thinned out) and a fingertip dilated. (For you non-preggo speak people, that means my cervix, which is normally thick and closed, is thinning and opening ever so slightly.)
Since week 36 I have taken Evening Primrose Oil (which is supposed to help dilate the cervix) once per day. At 37 weeks I took it one to two times per day, and now at 38 weeks I'm taking it 4 times per day. I've also been extremely horny and having sex regularly since the middle of last week. (Sex is also supposed to dilate the cervix.) Since my last check up, I've also been doing squats and other "position" techniques to try and move the baby lower in my pelvis.
My next appointment is on Wednesday, so we'll see what, if any, progress has been made.