I used to work at a pharmacy, and the "reminder" pills have no active ingredient in them, which is why you get a period. In fact, we had many women who would regularly skip them, and go months without a period, though I wouldn't necessarily recommend that.
If you'd like to avoid taking hormonal birth control, you can look into "Fertility Awareness Method" or "Natural Family Planning", to learn your body's signs and symptoms of ovulation/fertility (the book "Taking Charge of Your Fertility is an excellent place to start). This way you can avoid pregnancy without resorting to hormones, that may mess up your system or cause complications further down the road.