Track cycling event, more formally known as an elimination race. A massed-start race for up to twenty or thirty riders, with the rider who is last over the line every lap (or every N laps, depending on track size, number of riders and the desired length of the race) being eliminated until the last two remain to fight out a de facto match sprint. In the context of six-day races the competitors sometimes ride in their teams as per a madison, with handsling changes adding to the general confusion.
As the bulk of the action is at the back of the bunch, this produces a repeated telescoping effect as the rearmost riders close up and attempt to trap those ahead who thought they were safe; the chance of crashes is fairly high and the spectacle of the more tactically astute riders dictating affairs from the back of the race makes this a popular filler event with spectators and meeting organisers; it is however not considered serious enough to be included in the Olympics or World Championships.
Often referred to as just "a devil" for short, and also known in the USA as "lose-and-out" by contrast with the less successful formula of "win and out" where the overall winner is the winner of the first sprint who then drops out so the remainder can compete for second place and so on.
Update, May 2012
The elimination race has now gained a higher profile through its inclusion as one of the disciplines in the World Championship (from 2009) and Olympic (from 2012) omnium events