Period-havers of the world, unite! You have nothing to lose but your tampons!
The birth control pill works by preventing ovulation. Over the course of a natural cycle, your levels of estrogen will rise, thickening the lining of the uterus and eventually leading to ovulation; if the egg is not fertilized, you will shed your uterine lining and the unfertilized egg (the period). When you take the pill, your hormone levels are steady all month, so your uterine lining doesn’t thicken.
That means that technically you don’t have a period when you’re on birth control– even if you take placebo pills. Instead, you have withdrawal bleeding, which is the body’s reaction to not having the hormones it has the other three weeks in the month.
There is no evidence that skipping withdrawal bleeding will harm your health or make it more likely that you will get pregnant (or, for that matter, reduce fertility if you decide you want to have children). The most common side effect of skipping withdrawal bleeding is breakthrough bleeding or spotting, which usually stops as your body gets used to to its new, period-free routine. You might also find it harder to notice if you get pregnant; however, you can choose to have withdrawal bleeding every few months, have withdrawal bleeding that lasts only a day or two, or take a monthly pregnancy test.
The only reason birth control pills come with a placebo pack is historical. One of the inventors of birth control hoped that simulated periods would make hormonal birth control more acceptable to the Catholic Church and that women would find having a simulated period comforting.
If you want to stop having periods using the pill, you have two choices. First, you can get a birth control like Seasonale designed to reduce the number of periods you have. Second, you can start a new pack of birth control pills immediately after finishing the three active weeks in your old pack.