One of the best things I ever did in an RP was have my character accidentally kill them self out of the blue. Me and a mate got bored of this one particular plane-crash survival RP, and so we thought we'd do what would probably actually happen if a bunch of high school kids got stranded on a desert island and both killed ourselves by falling off of a cliff. 

That and Feral, an RP I was part of for like 5 years. It's still going technically, but my character got killed in fight with group's leader, once again, playing out what would actually happen when you have a violent killer who's getting progressively more unstable amongst your ranks.