Sometime around 1940, United States Air Force Doctor Harry George Armstrong, head of the Air Force's Physiological Research Unit (later renamed the Aeromedical Research Laboratory) recognized that humans could not survive under very low-pressure conditions, simply due to the fact that as atmospheric pressure lowers, so does the boiling point of water. At some point, the boiling point will pass below human body temperature, and saliva, tears, urine, and the mucous coating of the lungs start to boil. Then you die.
This is known as the Armstrong limit or Armstrong's line, and it sits somewhere around 18–19 kilometers (~11–12 miles or 59,000–62,000 feet) above sea level, depending on atmospheric conditions. At this altitude atmospheric air pressure drops below 0.0618 atmospheres (6.3 kPa, 47 mmHg, or 1 psi). At this pressure any pilot would have to be wearing a pressurized air mask regardless, to maintain blood oxygen levels, and the blood contained within the circulatory system is not affected, as it is not directly exposed to the air. If you were unprotected at this altitude you would lose consciousness quickly and die slightly less quickly, as your body would first not be able to take in enough oxygen from the ambient air, and then have the mucus coating of the lungs boil off, making recovery unlikely even if returning to normal pressures quickly.
Before one reaches the Armstrong limit hypoxia becomes a concern, somewhere around 4,500 meters (15,000 feet) in altitude; most airliners accommodate for this by pressurizing the cabin, but an oxygen mask will suffice if you are on a budget. After one passes the Armstrong Limit other problems appear; the water in your blood starts to turn to vapor, and nitrogen in the blood can cause decompression sickness -- the same bends that divers get from changing pressure too quickly. The Armstrong limit marks the point at which a full-pressure body suit (or, again, a pressurized cabin) is required, which, if well designed, should protect you from additional problems if the pressure continues to drop.