In my area, [these accidents](http://bicyclesafe.com/#wrongway) are way to common. I almost hit a biker like this the other day because they were riding against traffic past my apartment entrance.
[Here is a stack exchange question with some more stats on the topic](http://bicycles.stackexchange.com/questions/9033/why-is-it-s...)
Meanwhile, bicycles that go with traffic will (relatively) approach the driver at a much slower speed, giving the driver more response time.
The other issue with it is that it severely reduces your options. When riding with traffic, you can take the entire lane if necessary, something I have to do several times on my commute because the traffic flow around me is dangerous if I don't. Riding against traffic means you're stuck riding the gutter, somewhere I actively avoid on city streets if only to save my tires.
I don't ride with headphones, and shoulder check constantly to maintain awareness of what is behind me. My hearing has saved my ass several times (nothing quite gets your adrenaline going like hearing the roar of cabbie flooring his Crown Vic behind you in an attempt run your ass over).
Bicycling, like motorcycling, requires constant vigilance and awareness, it's naive to believe otherwise. It's tough to do and lapses happen all the time, but on a bicycle you don't have 5,000 lbs of metal and electronic nannies, just your wits and senses. And a U-Lock if it comes to it ;)
Edit: also, don't expect other cyclists to endanger themselves by swerving into overtaking cars for an against the flow rider. They might even consciously chose a good head-butt with the other rider over ending under a car. In other words: you should be _really_ ready to jump.
The other day, I was coming out of an alley, turning right on to a one way street. I'm turning right, so I expect all road traffic to be coming from my left. That's the direction I'm focused on in making my right turn.
Now, I always check to the right, but I never really expect to see anything. When I did actually see a cyclist zinging up from my right, it kind of gave me an adrenaline jolt. He was never in any danger, my car was fully stopped and never moved: but it was so unexpected to see him there, that i kind of went "oh god, I almost ran him over".
Point is: if safety is your concern, then probably the safest thing you can do is to follow the same laws cars do. Be where a driver expects to see another car.
It's ingrained in drivers to pay attention to the source of traffic in such cases, a sort of optimization tree for their merging decision. If you're traveling against traffic, you're an outlier not considered in others' equations, and you're at risk of injury.