You can breath at 35,000 ft without a pressured suit, but go much higher and you can't.
At sea level, you have 760 mmHg of air pressure. Oxygen is 21% of the air mixture, so you have a partial O2 pressure of 160 mmHg.
At 35,000 ft, air pressure is 179 mmHg [1], so if you breath 100% pure oxygen, you're getting the same amount of oxygen you'd get at sea level.
Go up to 50,000 ft and the air pressure is only 83 mmHg, so even breathing 100% oxygen, you're only getting 50% of the oxygen you'd get at sea level.
[1] http://www.engineeringtoolbox.com/air-altitude-pressure-d_46...