Why and how are always appreciated!
edit; as pointed out below
I would hasten to add a stipulation here. The richest person ever to be executed under the rule of law and not during a revolution. I think that's a more interesting exercise, as many regimes have been overturned throughout history.
Wealth can be hard to quantify, but Charles I, Louis XVI, and Tsar Nicolas II were all monarchs who lost their heads after some manner of trial.As monarchs, they commanded tremendous personal wealth, and had sizable kingdoms and empires besides. I'm not sure you can come up with an exact dollar value of their net worth, though.
This might be an unusual reference but part of the problem with this question is explained well in the rationale behind why Forbes magazine excludes royals and dictators from it's annual rich list:
We do not include royal family members or dictators who derive their fortunes entirely as a result of their position of power, nor do we include royalty who, often with large families, control the riches in trust for their nation. Over the years Forbes has valued the fortunes of these wealthy despots, dictators and royals but have listed them separately as they do not truly reflect individual, entrepreneurial wealth that could be passed down to a younger generation or truly given away.
Which is to say that for most political rulers throughout history it would be extremely difficult to distinguish personal riches from the state treasury in any meaningful way, but at the same time in any common sense definition of "richest" it would be hard to exclude the nobility/royalty.
Louis Buckhouse was said to have had an annual income of over $1 million when he was arrested, tried, and executed in the 1930s. A mobster by trade and contemporary of famous wiseguys like Charlie "Lucky" Luciano, Ben "Bugsy" Segal, and Meyer Lansky, he was said to have had about 250 people working the rackets on his behalf. That 1 million annual income would translate to roughly $17 million in today's dollars.
As far as I know, he is the highest ranking mafioso ever executed for his crimes in the United States, and might be the answer to this question for Americans. Although it's too recent for this thread, the Chinese have executed several individuals who may have had a similar net-worth.
Source: (behind a pay-wall) http://query.nytimes.com/gst/abstract.html?res=9B03E7DE123FE23ABC4E52DFB667838E629EDE
I'm surprised no one has mentioned Marcus Licinius Crassus. He was one of the wealthiest men in history. But in Roman culture, wealth was nothing compared to military victory.
Determined to stand on equal grounds with Pompey and Caesar, he pushed troops towards Partha, which... didn't go well. He died during a parley that turned violent when one of his officers suspected a trap. Crassus died during this scuffle, but it's rumored the Parthians poured molten gold down his throat.
I would hasten to add a stipulation here. The richest person ever to be executed under the rule of law and not during a revolution. I think that's a more interesting exercise, as many regimes have been overturned throughout history.
The problem as others have pointed out is that there are individuals for whom the notion of personal wealth and sovereign wealth are intertwined. Europes' Absolute Monarchs were so synonymous with the country over which they ruled that Louis XIV is widely reported to have quipped "The state is me" (in French, natch) -- ie to have asserted that there was no meaningful distinction between himself as a person and France as a sovereign state.
Louis XIV probably didn't actually say that, but the truth of the remark is in its endurance.
The eventual execution of Louis XIV's great great grandson, Louis XVI, is likely simultaneously the best known example of an absurdly rich person being executed and, at least nominally, the wealthiest person to have met that fate.
Of course, most of that wealth existed only on paper and was stripped from him well prior to his death. In the sense of his absolute monarchy -- while it lasted -- Louis XVI financed a goodly portion of the American Revolution out of what we might technically view as his personal slush fund (also known as the Treasury of France) owned... well... France, and called this pile of bricks "home."