Women who have personally experienced such blood clot problems as deep-vein thrombophlebitis, pulmonary embolism, cerebrovascular accident (stroke) or heart attack should not, under ordinary circumstances, take combined birth control pills. (estrogen and progestin)
For some of these medical problems, use of progestin-only birth control pills may be considered as they are not generally considered to increase the risk of recurrence. But even in this case, there is controversy and better alternatives are often available.
These medical issues frequently occur among women with predisposing risk factors. If the risk factors are eliminated, it is unknown just how dangerous it would be to take BCPs, but most physicians will not run that unknown risk for their patient, short of extraordinary circumstances.
Women who have a family history of these problems but who have not, personally, experienced the problems, may safely take BCPs.