The term runway excursion sounds like a family jaunt in the airplane, out to enjoy the scenic stripes on the tarmac and the Jet-A-scented breezes wafting down the runway. It actually refers to the event of an airplane leaving the runway by a method other than taking off or trundling down the appropriate taxiway. That is, over the side or the end.
A couple of weeks ago in Calgary, a JetsGo MD-83 went off the side of a runway after landing. The airplane continued rolling along the ground beside the runway and ran over a taxiway sign, before the crew took off again and returned for a normal landing. No one was hurt. Costly. Possibly career-ending. Bad for business. Embarrassing. Frightening for the passengers. Some speculate that the pilots aligned the airplane with what they thought was centreline lighting -- but Calgary doesn't have centreline lighting, only edge lighting. An official report will be issued in due course, but one never has to wait that long for uninformed opinion.
Today, there was a runway excursion at my home airport. Within two minutes of the first pilot saying, "hey, there's an airplane in the ditch!" at least seven pilots from three different companies were out on the tarmac, as close as we could get without entering the manoevering area. Everyone had at least one opinion on the cause and the extent of the damage. Airport staff and company maintenance personnel rapidly arrived to extract the airplane from the small ditch and tow it out of the limelight. And that was our excitement for the day.