Why is a lack of oxygen fatal to cells?
Here's an illustrated example in neurons:

ATP, of course, is generated by aerobic respiration. The critical biochemical reaction in the brain that is halted due to lack of ATP (and therefore O2) is the glutmaine synthetase reaction, which is very important for the metabolism and excretion of nitrogenous wastes:



The body uses this reaction to dump excess ammonia (which is a metabolic waste product) on glutamate to make glutamine. The glutamine is then transported via the circulatory system to the kidney, where the terminal amino group is hydrolyzed by glutaminase, and the free ammonium ion is excreted in the urine.



Therefore, as you'd expect, under hypoxic conditions in the brain, excess ammonia builds up which is very toxic to the cells. Neurons are also highly metabolically active, which means they generate more waste products. A buildup of nitrogenous waste products in the cell (and bloodstream) can be potentially fatal due to it's effects on pH (screws up enzymes and a whole slew of biochemical reactions).

In addition, the buildup of ammonia will cause glutamate dehydrogenase to convert ammonia + aKG to glutamate, which depletes the brain of alpha-ketoglutarate (key intermediate in TCA cycle). This basically creates a logjam in the central metabolic cycle which further depletes the cell of energy.

This is just one example of many. Of course, there are many, many other critical metabolic processes that require ATP (i.e. the Na+/K+ ATPase pump that regulates neuronal firing and osmotic pressure), but nitrogen metabolism was the first that came to mind :)