If there is a medical reason why labor must start, but you'd like to try some non-medical methods to induce labor, here are some self-induction methods (always discuss with your caregiver!). These methods also work to speed labor up!
1. Nipple Stimulation
Stimulating the mother's nipples causes the release of oxytocin, the hormone that contracts the uterus. Mom or partner can massage the nipples in many ways, using hands, warm towels, a breast pump, mouth, etc. If contractions become too strong with this method you should stop.
It is also a pleasant distraction :)
Orgasm causes the release of oxytocin (and contraction of the uterus) and may also release prostaglandins, a hormone-like substance that softens the cervix. Semen also contains prostaglandins, and sex is a more enjoyable way to deposit prostaglandins on the cervix than the methods used in the hospital! Once membranes have ruptured, however, avoid putting anything within the vagina (increased risk of infection).
4. Acupressure or acupuncture
Certain points on the body can be "activated" to start contractions. Make sure acupuncture is done by someone who is trained and always check with your caregiver first.
5. Bowel stimulation with castor oil
I've heard of this being used by cultures all over the world to stimulate labor. I've also heard of using a raw egg to induce vomiting, but that seems like it would be gross and unsanitary! Castor oil causes powerful contraction of the bowels (and diarrhea) which can help induce uterine contractions and maybe produce prostaglandins.
6. Homeopathic remedies
Make sure the person prescribing these knows what they're talking about. Herbal teas and oils, such as primrose oil can speed up contractions. Proper dosage and potential side-effects should be noted.
7. Changing Positions
Like walking, changing positions helps loosen up the shape of the mother's pelvis, takes advantage of gravity and may encourage the baby to wiggle into a more favorable position. Open knee-chest position, pelvic rocking, the lunge, side-lying, squatting, etc.