I posted this a few years back, but I don’t seem to recall that we hit upon a very satisfying answer.
Can money save you from the chair/table/firing squad? It would appear so, but I’d like to know EXACTLY how much… 
So, needless to say, but i will cheerfully say it anyway, please adjust for inflation and present your candidates.
cheers,
strsljen
One candidate might be Dr. John White Webster, who murdered fellow wealthy Harvard professor Dr. George Parkman (of the Parkmans) in 1849 and was hanged the next year.
King Charles I of England, executed in 1649.
King Louis XVI of France and Marie Antoinette, executed in 1793.
I’m pretty certain those dudes were not executed in the US.
Reading up on the link Webster was seriously in debt and even blamed his circumstances on living beyond his means. Net, I doubt he could afford an expensive defense team.
I’ve seen it maintained that the mobster Louis Lepke of Murder Incorporated fame was the richest man ever executed in the U.S. This sounds plausible, although I doubt that a mobster was what the OP had in mind.
Well some criminals tend to have wealth that is, how shall we say, off the record?
So even if their wealth didn’t save them from the gallows/chair/gas chamber you may never know how much money they had.
Prolly worth mentioning Thomas Capano who is apparently on death row in Delaware right now. He was an attorney; managing partner of a law firm; and from a prominent family in Delaware. So he probably has a lot of money. Of course it remains to be seen if he will be executed, but if he is, I imagine he will be somewhere on the top ten list of wealthy Americans to be executed.