SoloTwo: Actually, all hell does not break loose and your passengers don't begin to die at 13,000 feet. For healthy people, minor hypoxia does begin to set in at around that altitude and the effects become worse and potentially fatal as you continue to climb. Many a/c are capable of climbing into hypoxia altitudes that are not pressurized. To do so, they must be equipped with oxygen and, above certain levels, it must be used.
I no longer fly a/c that will not reach those rarified altitudes so I don't remember off-hand the altitudes at which oxygen use is required. It is required at a somewhat lower altitude (12,500 feet MSL?) for flight crew than it is for passengers. There is also a time restriction for flight crew to use oxygen if they are going to fly at a borderline altitude. I don't have the time now to look it up but anyone could do so by googling the US Federal Air Regulations and using their keyword search function for oxygen.