Crucifixion was a punishment used in ancient Rome to execute criminals. The most notable crucifixion in history was that of Jesus Christ, an image of which was preserved on a crucifix. (VOY: "The Omega Directive")
Metaphorically, one could be said to crucify oneself; that is, to punish oneself needlessly for something one felt they were at fault for. In 2293, James T. Kirk urged Spock not to do so in the aftermath of Kirk's and Leonard McCoy's being tried for the murder of Chancellor Gorkon. (Star Trek VI: The Undiscovered Country)