Riding against traffic is both totally illegal and totally dangerous. Bicyclesafe.com says the following about riding against traffic (see Collision Type 4):
Don’t ride against traffic. Ride with traffic, in the same direction.
Riding against traffic may seem like a good idea because you can see the cars that are passing you, but it’s not. Here’s why:
1. Cars which pull out of driveways, parking lots, and cross streets (ahead of you and to the left), which are making a right onto your street, aren’t expecting traffic to be coming at them from the wrong way. They won’t see you, and they’ll plow right into you.
2. How the heck are you going to make a right turn?
3. Cars will approach you at a much higher relative speed. If you’re going 15mph, then a car passing you from behind doing 35 approaches you at a speed of only 20 (35–15). But if you’re on the wrong side of the road, then the car approaches you at 50 (35+15), which is more than twice as fast! Since they’re approaching you faster, both you and the driver have lots less time to react. And if a collision does occur, it’s going to be ten times worse.
4. Riding the wrong way is illegal and you can get ticketed for it.
One study showed that riding the wrong way was three times as dangerous as riding the right way, and for kids, the risk is seven times greater.