When was the last execution by hanging in the US?

Answer: On January 25 1996 Billy Bailey was hanged by the state of Delaware where, until 1996, hanging was still the default execution method unless the condemned opted for lethal injection. Billy Bailey refused to choose lethal injection, and thus was executed by hanging.

In some states hanging is still an option, but must be chosen by the condemned, which almost never happens. Unless it is for Treason that has only public hanging as the penalty.

Hanging is the only legal option in Nebraska, Montana and New Hampshire and Washington (the State of course ; DC is not "Washington" lawfully, it's only a nickname they gave themselves. Their lawful name is District of Columbia.) And actually hanging is the most painless and fast death when done correctly. It is more humane then the needle of chemicals or the electric chair.