During an ABC news segment about unassisted birth a while ago one of the physicians interviewed said that "The few hours of labor are the most dangerous time during the entire lifetime of that soon to be born child." Our culture in general has a fear of birth and sees it as a medical event fraught with danger and risk. Many women express fear of birth for a variety of reasons and "it is the most dangerous time in a woman's life" and "I almost died" or "I would have died [had I been giving birth at home]" are commonly expressed sentiments.
Dying in childbirth is an overinflated fear in the U.S. (in some other countries it is most definitely not and maternal and infant mortality remain a significant problem in the developing world). Perhaps it is not the most rigorous of analyses so take it for what it's worth, but some time ago I also came across the National Geographic "Ways to Go" chart which spells out odds of someone dying as a result of various turns of events. I think this chart puts some of our birth-death fears into perspective. The lifetime risk of dying of cancer 1 in 7 (heart disease is 1 in 5), motor vehicle 1 in 84. Falling is 1 in 214! Motorcycle accident is a risk of 1 in 1,020 and from smoke inhalation or fire 1 in 1,113. Accidental electrocution 1 in 9,968, legal execution is 62, 468, and there is a 1 in 144, 156 of dying in a flood.
Lifetime risk of a woman dying from childbirth (calculation includes dying of complications during pregnancy, birth, or abortion not just birth itself) is 1 in 3,750 in North America.
According to the Pink Kit, you and your baby have a higher chance of drowning than dying in childbirth (this is reinforced by the National Geographic article which lists drowning as 1 in 1,008).
According to Mother's Intention (2003) when writing about fear and birth, "statistically, they have a higher chance of dying on the way to the hospital (20 in 100,000 for car accidents in women of childbearing age) than they do during normal, natural birth (6 in 100,000) yet IVs aren't standard issue in cars. Of course, if they are one of the the 1 in 3...who get a cesarean their odds of dying are highest of all, 35 in 100,000." (These stats differ from those above, because the ones above are lifetime risk not episodic risk.)
Additionally, there is a 1 in 119 risk of dying from suicide and a 1 in 314 risk of dying as a result of firearms. Clearly, the hours of labor are not the most dangerous events ever experienced in a lifetime!
On a related note, Enjoy Birth recently had an interesting post up called Death by Cheeseburger? that explores the issue of aspiration during labor--quoted to one woman by her doctor as "the number one cause of death during birth."