How would the human body be affected if the oxygen levels on Earth suddenly decreased by 15 percent? This is instant. Not over time. How would we adapt? Would some people die and some not?
If you mean it we lose 15% of current concentrations, to %17.85 it will be harder to breath we will have a harder time concentrating and thinking. Many more people would need to be put on Oxygen to survive, many smokers and others with lung and blood issues would likely die before they knew what was wrong. Some of it might depend on what replaces that missing %3.15 if it disappears because of combustion and is replaced by CO2, while not immediately fatal, combined with the lower Oxygen content could be devastating to most animal life. The healthiest would likely be OK, and those living in very green areas, forests, crop fields etc would do better (assuming the sun is out and plants are doing their thing, if it was a large fire that caused it, there might be no sun for a while, so the plants would be sucking up Oxygen too).
if you mean total Oxygen drops to %6 then those without access to Oxygen masks are pretty much goners.
some useful info here. http://classroom.synonym.com/minimum-oxygen-concentration-human-breathing-15546.html
Denver has about 17% less oxygen than at sea level. Note that this isn't reduced concentration; there's just less air. This answer doesn't address the increased proportion of other elements in the air, only oxygen reduction.
According to this article on altitude sickness, the first effect that kicks in from reduced oxygen is hyperventilation -- you breathe faster in an attempt to get more oxygen into your lungs. This can lead to weakness, dizziness, and fainting. More-severe symptoms can occur at higher altitudes (= lower oxygen levels), from vomiting and headaches to pulmonary edema and brain injury.
Obviously it's possible to acclimate -- people live in Denver, after all. So the main challenge seems to be the transition -- those first few days after the oxygen drops are going to be challenging. But people who avoid strenuous activity for a few days and take some extra care with diet and medications can adjust.
A sudden 15% drop is like everybody hopping a plane to Denver -- uncomfortable at first, but with care it's not likely to do long-term harm. Of course, people who are already medically fragile might suffer worse consequences.
Humans routinely experience a loss of more than 15% of the available oxygen in a matter of minutes with no harm done. It's called flying in a plane.
Note, however, that it looks like there might be a relationship between long term lower oxygen levels and depression.
Google "hypoxic air technology for fire prevention" for a lot of pertinent information.
If some oxygen in air at normal pressure is replaced by nitrogen, one effect is that fires become much harder or even impossible. It also reduces the rate at which paper oxidizes. This technology is therefore used in archives of valuable paper documents. Down to 13% oxygen or thereabouts there are no health problems caused in the very short term to healthy people entering the archive to retrieve documents, and desk-working in the archive for hours at a time is also not known to be harmful. You'll breathe faster to compensate but may well not notice. People with severe chronic respiratory diseases are affected adversely, as with flying or altitude.
In the longer term ( days to weeks) I would expect that acclimatisation takes place if one works in such an archive, just as it does if you travel to a higher altitude. The body makes more red blood cells, basically because each is carrying less oxygen. This can have adverse health implications, mostly small increases in risks of serious cardiovascular events.
One important point. If you are considering a low oxygen planet then that is a planet where intelligent life almost certainly never got past the stone age. This is because natural fires would scarcely exist and making fire by friction would probably be impossible. No fire, no metals. No metals, no higher technology. Probably.
Only less than 6.25% of oxygen decrease will allow humans to live. Any less oxygen than this will not support human life. This decrease of oxygen will increase carbon dioxide content by 2500 times and that will increase atmospheric temperature by about about 125 degrees Fahrenheit, which is not suitable for human life.