Is there anyone who should not have birth control pills?

Yes. Birth control pills with estrogen should not be used by women over 35 who smoke, women with a history of a blood clot or an increased risk for one. They should not be used by women who have vascular problems or active liver disease or gallbladder problems. They should not be used by women with breast or uterine cancer. You can use estrogen-free birth control however.
Yes. Most women can safely take birth control pills, but if you are pregnant, have high blood pressure, have had blood clots, a stroke or heart attack, certain kinds of cancers (breast or uterus), active liver disease, migraine headaches with aura, are a smoker and over the age of 35, and a few uncommon medical conditions, you should not take birth control pills.