The first happened at a show in St. Louis. After a man in the audience was spotted taking pictures, Axl Rose angrily demanded from the stage that security confiscate the camera. When they didn't respond as fast as the singer was hoping, he decided to jump into the crowd and handle things his own way, which included tackling the man, taking his camera, and punching several audience and security members before getting pulled back onstage by members of the band's own road crew.
That part didn't last much longer, though. Rose simply picked up his Mr. Microphone and bailed. The Wikipedia page claims it happened at the 15-song point in the set, but it also says that includes guitar and drum solos, which is like saying bathroom breaks count as songs, too.
Anyway, fans apparently felt that they had not received a sufficient amount of rock for their money and promptly started tearing shit up. The incident came to be known as the "Riverport Riot," taking its name from the amphitheater where the chaos broke out.
The name was changed to the "UMB Bank Riot" in 2002 before taking its current name, the "Verizon Wireless Riot," in 2006.
That wouldn't be the end of the band's property-destroying ways. During a stop in Montreal on their co-headlining tour with Guns N' Roses, Metallica frontman James Hetfield nearly set himself on fire by absent-mindedly standing on top of a pyrotechnics display just as it was beginning to shoot heavy metal flames toward the sky.
It's an easy thing to miss if you're not looking for it.