I never got past 39 weeks with any of mine- but my dear friend swore by using a breast pump. She was 10 days over due and she used the breast pump for about 2 (!) hours and went into labour that night- she was due to be induced the next morning.
With DS1 my waters broke at 35 weeks, but labour didn't start, so they wanted to wait as long as possible before inducing me. I was on bed rest to prevent infections, and it was a miserable experience. I was going to be induced at 36 weeks, but I had a very spicy curry and labour started on its own! I know that is an old wives tale but it worked for me. Having said that, my labour didn't really progress very well so I had to have pitocin.