I stumbled upon this thread whilst looking for information regarding maximum operating altitudes for commercial air ambulances with seal level cabins. Whilst Therac's answer is great I would suggest that its not the whole picture.
The majority of the work on the physiological consequences of aircraft cabin altitude was done by a Professor John Ernsting (who I had the great pleasure of meeting on several occasions) at Kings College in London. His work in aviation medicine was extensive and he was responsible for working with aircraft engineers to set the maximum acceptable cabin altitude for commercial cabins. Hypoxia is, as Therac points out, the physiological driver for this decision, but the goal was to set the bar well below the threshold for hypoxia induced cognitive impairment.
When we skydive above 10,000 ft AGL (in unpressurised aircraft) we tend to stick to the EASA guidelines of greater than 30 minutes of planned exposure above 10,000 ft requiring individual access to supplemental oxygen, but this is widely flouted in my experience. It is well known that there is considerable variation in the susceptibility to hypoxic environments from person to person.
Back to the commercial cabin. The basis of the 8000ft decision for commercial cabins was that at this altitude the haemoglobin / oxygen dissociation curve is in its flat portion. The curve represents the saturation of haemoglobin in the blood at any given partial pressure of oxygen in that blood. As the cabin altitude rises, the pressure falls and, if you like, less oxygen is driven across the alveolar membrane into the blood. This leads to a lower arterial oxygen pressure (Pa02) and therefore less saturated haemoglobin.
The curve is sigmoid (s shaped) in nature and flat at the highest Pa02. In other words, decreasing the Pa02 does not, initially, have much effect on the percentage saturation of haemoglobin. This is the area that is targeted by the 8000 ft cabin altitude. Raise that altitude significantly and you are on the steep part of the curve and haemoglobin saturation falls precipitously, lower it and you don't get a significant physiological advantage (because the haemoglobin is already between 92 and 98 % saturated).
So yes, its all about hypoxia and the cost benefit of maintaining a particular cabin wall differential pressure (and therefore cabin altitude). Of note is that modern aircraft tend to run their cabins at slightly lower altitude than 8000 ft - in the order of 4000 - 5000 ft. This gives slightly more physiological tolerance for those passengers with pulmonary disease without being over burdensome on the pressurisation packs or cabin wall life.
In line with the guidelines (I just read before posting) I'm an aviation physician with an interest in commercial patient transfer in the UK.