None, in my opinion. I hate them and the Harry Hairshirt philosophy behind them. The biking equivalent of a neocon: wishing for simple solutions to a complex world.
Proponents talk about how it cleans up your stroke by demanding a smooth style, how light weight and bulletproof they are and how direct the pedal response is. When you want to go fast you have to stand up and muscle it: forget cadence or timing, it's just pump til you bleed.
You stop by backpedaling! Ever try to stop with just the rear wheel? That's the idea. Traffic anyone?
There's a reason to have all the things, like gears and brakes, they are missing. It's just a stupid fad.