I love this kind of thing: Boing Boing: Brooklyn residents: just say no to space elevators!. Along those lines there is a fiction contest going on at the ESA centered on their elevator project. I'm considering entering, but the ideas I've been having for them are all pretty grisly. Murder mystery on the elevator (A classic locked door situation)? Horrible plague on the Elevator? Oxygen leak? Explosive decompression investigation? Terrorist attack (props to Fred Pohl) ? Elevator Rave (picture lots of x cruching perky goths swaying to apocryphal music on their way to a concert topside...).
Unfortunately, none of these would win.