It depends, of course. Ideally, an atmosphere would be 21% oxygen with no toxic gases. However, we do have some wiggle room. With the same air pressure as Earth, we can survive down to about 16% oxygen for short periods, and more than 21% is fine. While pure oxygen for long periods is detrimental, double or even triple 21% is fine. The critical insight here is to break it down by formula and pressure. While Earth’s atmosphere is 21% oxygen and 78% nitrogen, it can vary so long as there are no toxic gases. For long term breathing, we’re used to 21%, and need at least 18%. However, atmospheric pressure is just as important.
For pressure, which allows us to breathe easily, the psi at sea level is 14.7, but people live at higher altitudes where the air is much thinner. Our highest populated peak is La Rinconada in Peru, where the atmosphere is 7.93 psi and they do just fine at 21% oxygen. Perhaps obvious, but a profound take away about the future is to imagine a planet with, say 5 psi, which is very low pressure for us, but the percent of oxygen was higher, say 50%, we might be able to breathe just fine. If we’re lucky enough to visit other planets, these are the types of things we’ll need to look at. Perhaps living on a planet comprised of 33% oxygen, 50% nitrogen, and 17% argon, with an air pressure of 8 to 10 psi might be a part of our future.