Thick E,
The same percentage of oxygen exists in the atmosphere at high altitude vs. low altitude. The difference is that the air is more dense at lower elevations, and the atmosphere has greater pressure...the oxygen in the atmosphere has more pressure ("partial pressure") with which to pass through the membranes in our lungs and into our blood stream.
As we climb higher and higher, the air is less and less dense, and is under a lower and lower pressure as well. The same percentage of the atmosphere is still oxygen (approx 21%)...there's just less atmosphere, and less pressure.
In order to ensure enough pressure for us to breathe properly and respirate, we pressurize airplanes. We do this by compressing the atmosphere in the aircraft engines, and piping it into the cabin as "bleed air," or air which is bled from the engine compressors.
When the air is compressed, it becomes very hot. It leaves the engine compressor around 600 degrees, and is cooled along the way by various means. It's still too hot for use in the cabin, so we use air conditioning machines, called air cycle machines, to adjust the temperature. Part of the air conditioning process involves cooling the bleed air we use for pressurization, and part of it involves using warm bleed air to then fine tune the cooled air to the desired temperature. The fine tuning is done outside the air cycle machine by several methods at the same time, including bypassing the air cycle machine with warm air, and injecting warm air downstream ("trim air").
To regulate the pressure in the cabin, one or more "outflow valves" open and close to slow the rate at which the air can leave the cabin. Depending on the aircraft size, the entire cabin airflow is replaced every twenty seconds to every minute or two...as air is constantly flowing into the cabin, and leaking out through the outflow valve. The amount of pressurization that's held is varied by changing the size and opening of the outflow valve.
What this means for you in the passenger cabin is that you're constantly receiving fresh air from outside the aircraft. The air you exhale is quickly vented overboard, and a constant supply of fresh air is being piped aboard. You scarcely notice the change, but just as air is being piped into the cabin, it's also being vented back out. Simply put, you won't run out of oxygen in the pressurized cabin air because it's constantly a new supply...and given that you're high up above most polution, it's some of the cleanest air you'll breathe, too.