Birth control can help prevent certain types of cancers.
It does affect your menstruation cycle, which is why many women get on it. I got on my pill originally because my periods were debilitating. Seven days long, heavy, blood clots, nausea, back pain, severe cramps. With the pill, they became three days in length and light to moderate in flow. Cramps lessened, nausea went away as well as the majority of the back pain. Some women try to use it to help regulate their periods as well.
Some women do find themselves getting larger or smaller breasts, some women experience weight gain, and others find it does nothing to their physical appearance. It's all going to depend on you! I personally found it had no affect for me appearance-wise.
There are side effects with the pill, however. There is a risk of blood clots, which is severely increased if you are a smoker. It's highly recommended not to take hormonal birth control if you smoke. It's also ill-advised if you experience migraines with auras.
I have a friend who took Yaz or Yasmin and ended up with a pituitary cyst. I'd really recommend one that's been on the market more than 10 years. Its side effects are more well known at that point.
Sometimes you can experience breakthrough bleeding (bleeding between "periods") if you are not consistently taking the pill. Some women it's if you're late by a few hours, others a few days. I would recommend a cell phone alarm to help you remember to take it the same time daily. Breakthrough bleeding is a real hassle as it can last a really long time sometimes. Not a worry if you're good at taking it, usually.
Some women do experience mood changes and have to try a lot of pills before finding one they can handle.
As far as further effects on your cycle: your period technically isn't a period on it but rather breakthrough bleeding due to the drop in hormones. Birth control is believed to work by 1) thinning the uterine lining (hence, the lighter flow many women experience) and 2) preventing ovulation.