For most people effects of having not enough oxygen would be at around 4.5 km. Some people are able to train themselves to sustain these effects, though but just very few can breath unassisted above 8 km.
I would say the absolute limit is 18 km, above this altitude the atmospheric pressure is so low that water boils at temperature of human body. That means you would lose consciousness in just few seconds.
Hope this answers your question to some extent! 🙂