The best male birth control I am aware of is cotton root bark. If taken regularly over a 6 month period it is said to cause permanent sterility in males. As an added benefit is increases the strength of orgasms by increasing oxytocin levels.
For females stone seed will do the same thing if taken daily over 6 months.
If you are not looking for permanent birth control then there are other options that work temporarily.
Juniper berries are used by the Indians as a means of birth control. I have heard it being used for three consecutive days before intercourse, or a large dose after intercourse.
Wild yam is said to work as well as birth control pills but like the pill takes about a month to fully build up. It also takes fairly high doses (about 9 capsules daily, which works out to about 1.5 teaspoons daily). If you can find a concentrated extract this will reduce the amount needed.
Gotu kola is a natural spermicide as are vitamin C (ascorbic acid) and citric acid. Gotu kola would be best used as an extract made in to a suppository. Semen is actually alkaline to help it survive the slightly acidic pH inside the vagina. Increasing the acidity with the ascorbic or citric acids makes the environment too acidic. The tricky part is not making it too acidic that it irritates the sensitive mucous membranes. I heard cases years ago where women were actually inserting vitamin C tablets in to the vagina but these were burning the tissues. Making a weak acid solution then squirting a little in to the vaginal cavity would be a safer means of doing this .
Keep in mind though that birth control, natural or otherwise, is not always 100% effective.