Why do neurons die so quickly (relative to other cells) when deprived of oxygen?
There is a good review in the Journal of Experimental Biology (Bickler and Donohoe 2002, JEB 205, 3579–3585) I will just summarize for those that do not have access to the review.

Neurons use lot of energy to maintain their polarized state, this is not required to other cells. When O2 or blood flow is reduced, the neuronal ATP levels breaks down very fast, with 90% ATP depleted in less than 5 minutes. Without ATP, the neuron can not maintain the correct ion flux, so depolarization occurs causing glutamate excitotoxicity, cell swelling and finally cell death.