Whenever we watch the Saw movies, or a particularly gruesome episode of The Tudors, people bite the big one in extremely awful ways. Although the sight is repulsive, we still want to take a peek because we're a little bit curious. What would the scariest kinds of death be like, and how long would they take?
In the US, hanging is still a legal mode of execution in some states. The last hanging was conducted in 1996. In a modern hanging, death should be instantaneous due to a broken neck. The knot of the noose is placed under the prisoner's jaw, pulling the neck backwards as the body falls forward and down. It's over in a fraction of a second. A prisoner's weight has to be used to calculate the exact length of the drop. The ideal force to break the neck is 1,260 foot-pounds and the length of the drop is 1,260 foot pounds divided by the body weight of the prisoner in pounds. If the drop is too long, the victim can be entirely decapitated. This is still preferable to too short a drop.
The 'short drop' a sadistic version of hanging, can take up to 45 minutes of slow asphyxiation. When the body's fall is too short, the neck doesn't break. The air isn't even completely cut off. Instead, the noose constricts slowly. This can also happen if the rope isn't boiled and stretched to make sure it doesn't stretch like a bungee cord instead of pulling people up short. The victim's neck muscles may also be too strong, and the rope may not be lubricated enough to slide over skin and pull up quickly. Even in the modern era, when such things are calculated, some executions go wrong in precisely this way.
The gas in the gas chamber is hydrogen cyanide. This stops cellular respiration. Although it was ruled a humane method of execution, there have been several convicts who explicitly indicated pain during the process, often for several minutes. Doctors say that, since the process cuts off oxygen, it would decrease the flow of oxygen to the heart. Ideally, the oxygen to the brain would be cut off soon enough that victims don't feel it, but they would be experiencing the same pain and pressure sensations that people feel when they're having a heart attack. Victims often also indicate that they feel strangling sensations.
The last state to use the electric chair was Nebraska. It was the state's only method of execution until 2008, when Nebraska's Supreme Court ruled it inhumane. It was invented before the long drop method of hanging was widespread, and so at the time considered a more humane way of executing prisoners.
Although the process is meant to be a quick jolt of between 5 and 20 amps and 500-2000 volts, which should kill someone instantly, the jolt has on occasion had to be repeated several times because the heart was still beating. The body overheats, essentially cooking, and there are reports that bodies have caught fire. Because electricity stimulates the muscles, the jolt also cause the body to convulse violently enough that bones are broken and ligaments torn. Immediately afterwards, the body is too hot even for an autopsy, and will burn the medical examiner either through direct contact or through steam if it is immediately opened.
This may be a good way to go, comparatively. In some cases, people may not breathe in water at all. The throat constricts to the point where the person cannot inhale, and they asphyxiate themselves. In other cases, water is inhaled. Resuscitated drowning victims report that after the pain and pressure, they actually feel calm, warm, and pleasant when they drown.
It's the lack of oxygen to the brain that results in the high - the same method is used by people to get lightheaded by wrapping something around their necks, or even deliberately hyperventilating. Drowning is still a difficult death, if only because there is no way for a victim with a distorted time sense to measure how much of a high they feel versus how long they spent painfully suffocating.
There was a popular rumor that a head could stay alive for thirty seconds after it was separated from the body, provided the separation was clean and quick enough. That has been pretty thoroughly debunked, on this site even. A broken neck generally renders someone unconscious and leads to death so quick it might as well be instantaneous. A severed neck would do the same.
The real trick of the beheading was to have an executioner both skilled enough and willing enough to get the neck on the first try. This is why many victims paid their executioner beforehand. Still, you couldn't exactly ask for your money back after a couple of hits with an ax. Last-minute bribery didn't always work, especially since the headsman was paid by people who hated the executed enough to want to kill them. Many victims asked people in their family, or on their side politically, to be there on the day of their execution so the headsman would face public disapproval if he did a sloppy job. There are tales, however, of hungover executioners needing seven or eight blows with an ax to finish.
Hypothermia is the most eerie death, from the perspective of the people finding the bodies. There are people who have died in the manner of To Build a Fire, fully aware that they were losing limbs and slowly freezing solid. The rest of the stories aren't as cut and dried. The body temperature slowly drops and the person, although they do feel cold, don't notice how bad it is until they're delirious. People are found dead of hypothermia, floating in popular lakes and rivers where they were wading and swimming, able to get out at any time.
Another danger of hypothermia is re-heating. When people get too cold, the blood retreats from their extremities in order to conserve heat and keep the internal organs warm. If they're heated too quickly, the body dilates the blood vessels in the extremities. The blood rushes into them and the cold tissue cools it drastically. It then circulates back into the torso and cools the organs until they shut down.
The strangest thing about freezing to death is people often feel like they're boiling alive. Rescue personnel find hypothermic people outside tents, stripped down completely, in sub-zero weather. This is also due to dilation of the blood vessels. Even if there is no warm stimulus, the muscles constricting the blood vessels will eventually tire out. When they do, cold blood runs back into the body, but warm blood flows out to the extremities. The difference between the warm blood and the cold tissues is extreme enough to make the person feel like they're too hot. A hypothermic person is also often irrational, so they will undress themselves as a way of relieving the intense heat they feel without considering the causes and consequences.
This is the one no one wants, for very good reason. It's obviously terribly painful, but could be made more or less so depending on the circumstances. The very best circumstances were ones in which a large number of people were burned at once. This necessitated a large fire with a lot of smoke. Smoke inhalation is what causes most deaths in house fires, and the people who die of it generally are sleeping and never wake. People in the middle of a big pyre could inhale the smoke and knock themselves out before they were burned. Another way to speed the death was for a friend of theirs to add some gunpowder or other explosives to the mix.
The less fortunate were burned slowly, and stayed alive until the fire shut down their internal organs, or until they had lost enough blood in the burnt areas of their body. Occasionally someone died of shock. The least fortunate of all were burned to death superficially and slowly. There are some accounts from the middle ages that say they were alive for hours. Makes hanging look pretty good.