I was trying to explain to someone why the cabin is pressurized (no one wants hypoxia) and that led to discussion about the emergency oxygen masks available on airliners.
If a person didn't put on their oxygen mask, would they be able to survive the lack of oxygen while making an emergency descent to a safe altitude? Would they sustain severe brain injury?
Within 30 seconds (oximeter 100-95): noticed physical symptoms beginning. I could tell that something was wrong, but felt functional.
Within 60 seconds (oximeter ~90): mild headache. Still able to write my name. Not feeling good, but acceptable.
Within 3 minutes (oximeter ~80): Able to do simple tasks when specifically directed (thread a nut onto a bolt), but completely unable to multitask at even the simplest things (tried to put my pen down...didn't notice that I missed the desk - it landed on the floor.)
Within ?? minutes (oximeter ~70): I am no longer able to perceive the passage of time. No longer able to take meaningful notes. My signature is still legible - instinctive muscle memory apparently doesn't degrade nearly as fast.
Within 6 minutes (oximeter unknown): I have taken another pen from my pocket and am playing the knife game from "Alien" with it. This is much more interesting than paying attention to the directions from the instructors. I don't notice anything odd about my behavior.
Immediately after: An instructor gives me a direct command to put my mask on. I comply.
So, to answer your question: It depends. I can safely say that seven minutes at 30,000 foot environment won't guarantee death (because I've survived it), and it won't guarantee severe brain injury (they let me keep flying) but on the other hand, I'm young and I exercise. The best answer I can give is the same one that applies to scud running:
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Short answer? It's entirely possible that not putting on a mask could result in death.
Long answer:
The classic example of hypoxia is the Payne Stewart Learjet crash that happened in 1999; the jet lost cabin pressure (and the crew lost consciousness) sometime in the 6 minutes between 23,000 feet and 36,500 feet. All 6 aboard perished in the crash.
From the NTSB report, which the Wikipedia article quotes:
Research has shown that a period of as little as 8 seconds without supplemental oxygen following rapid depressurization to about 30,000 feet (9,100 m) may cause a drop in oxygen saturation that can significantly impair cognitive functioning and increase the amount of time required to complete complex tasks.
There are tables available that show time of useful consciousness. Above FL300 (30,000 feet, or around 9,150m), a healthy human will have less than 3 minutes of useful consciousness. Prolonged hypoxia, at any altitude, can have serious repercussions. The National Institute of Health states that "[some] brain cells start dying less than 5 minutes after their oxygen supply disappears. As a result, brain hypoxia can rapidly cause severe brain damage or death" (source).
That would depend on at least the following:
how high the cabin got during the process
how long it stayed high
the physical condition of the passenger
perhaps to some degree how much oxygen was coming out of the masks of adjacent passengers
I went through NASA's altitude chamber program at the Johnson Spaceflight Center back in the early 80s. They wouldn't take the chamber higher than 25,000 for civilians. I was in very good shape back then (hard to believe now) and stayed functional the longest, but when they finally told me to put my mask back on, they told me I only got it half way to my face. An instructor had to come over and assist me.
Did I suffer brain damage? Some might contend I did.
Seriously, I Googled "survivability at high altitudes" and saw lots of info.
The other answers focus on the physiology of failing to put a mask on, but I am going to offer another take on this.
Whether you die from not putting on a mask depends on one thing: Did the pilots get their masks on before useful consciousness ran out? If they did, you live. If they didn't, you die. It is as simple as that. In the case the pilots get their masks on and no one else does, they will initiate an emergency descent. This descent is typically initiated from memory items and not a checklist, so it can be initiated quickly. The goal of the emergency descent is to be at 10,000 ft iASAP (for us the goal was under 4 minutes), and many jet aircraft can get there faster. The only regulations I am aware of regarding the descent is that you must be below 25,000 ft in under 2 minutes (25.841; assuming complete loss of cabin).
If the emergency descent is initiated and in all likelyhood it won't matter if you put the mask on or not, you'll wake up during the descent and it'll only have been a few minutes. Its always better to put the mask on, but it won't be the deciding factor, the pilots masks will be.
I'll also point out the O2 masks the pilots have are vastly different than those the passengers get. Pax get chemical O2 generators that last about 15 minutes once activated (by pulling the tubing down) and attatch with a flimsy rubber band. The pilots get quick-don masks fed by an O2 cylinder. To don the masks you simply grab it, the O2 pressure inflates the webbing around the mask. Then you slip it on your head, let go of it and the mask compresses around your face. Twist the mask regulator to Emergency and you have positive pressure forced flow O2 for the descent.
§25.841 Pressurized cabins. (a) Pressurized cabins and compartments to be occupied must be equipped to provide a cabin pressure altitude of not more than 8,000 feet at the maximum operating altitude of the airplane under normal operating conditions.
(2) The airplane must be designed so that occupants will not be exposed to a cabin pressure altitude that exceeds the following after decompression from any failure condition not shown to be extremely improbable:
(i) Twenty-five thousand (25,000) feet for more than 2 minutes; or
(ii) Forty thousand (40,000) feet for any duration.
