The Miami Incident
Jim Morrison's career is peppered with controversial moments, mostly in live settings with thousands of witnesses. The infamous (legendary?) Miami incident of 1969, however, stands tall above the rest of his shenanigans, and is made almost mythical based on the varying accounts of what actually happened.
What's known is The Doors were supposed to play a show at the Dinner Key Auditorium in Miami, and that Morrison had spent all day drinking and flying on planes. He stopped singing shortly into the beginning of the band's set, and continued by yelling obscenities and going on drunken roller-coaster rants about love & hate. Eventually, he began stripping his clothes off, and that was when he allegedly exposed himself to the crowd.
He was arrested and convicted five days after the show for indecent exposure, among other charges, and sentenced to six months in prison with a $500 fine (around $3,200 in today's money). He died before he could serve his sentence, which just kinda leaves the whole incident hanging over Miami's coconut grove district and The Doors' career.
By Dade County Public Safety Department [Public domain], via Wikimedia Commons