At what level of current are you likely to be in danger of death?

The level of current you are most likely to be in danger of death depends on the path of current flow through your body, and on the frequency of that current.

With sufficient current, there is always the danger of burns, usually on the surface of the skin, which is particularly an issue with high voltage.

The most sensitive organ is the heart. Interestingly, frequency is a big factor. If you were to apply DC, it would simply stop and then start, assuming you did not apply enough to cause internal damage. If you were to apply AC, with the right frequency, and with just the right current, you can do irreversible damage to the heart's pacemaker, the sino-atrial node. The heart would then enter irreversible ventricular fibrillation, and you would die.

It turns out that the most dangerous current is about 1 ma, at 60 hz, applied directly across the heart. Depending on external skin resistance, this translates to around 120 AC, 60 hz, applied from hand to hand, with the current path through the chest.