This one was a lot funnier watching it than it is explaining it, but during Havoc 95, during the Randy Savage/Zodiak (?) match, some drunk dude hops out of the crowd and starts going after Savage. He tries to get into the ring, but is immediately tackled by security. Savage knocks Zodiak to the floor, and when he follows him out, the man breaks free, darts into the ring and just lunges at him but misses and gets tackled again. And he was still going after him while he was out on the floor...and what made it so funny was that it went on for about half a minute before the commentators even acknowledged him...they were just calling the match like nothing happened and I found it pretty funny.
International Incident 96 was probably my all time favorite run-in. First, before the match, a bunch of fans fall over the guardrail trying to get at HBK while he's making his entrance (the actual guardrail fell over, causing them all to spill over into the aisle). Then, during the match between Camp Cornette (Vader, Owen and Bulldog) and HBK, Ahmed and Sid, Vader had Shawn in a reverse chinlock, when suddenly some guy starts climbing the top rope. Suddenly, Bulldog, Owen and Ahmed just rush the dude, and he hops down and gets carried away by security. That had me dying.
On an episode of Raw in late 99, Jericho and Rock were out for one of those "insult trading" promos, when suddenly, some guy dressed like Jericho rushes the ring. When he's carried out, Rock grabs the mic and tells Jericho "Keep your jerkoff dad out of the ring!"