It seems many casual cyclists believe that if you ride against traffic, you see them and they see you, making cycling safer. However, this is not the case. Let's look at the math:
If you ride against traffic, the speed at which cars are approaching you is increased by a factor of (car speed + bicycle speed) / (car speed - bicycle speed). At average cycling speed this factor ranges from about 1.5 to 3. This gives both parties far less chance to see and avoid each other, less time to brake and, in the event of a collision, it results in an impact speed of between 30 and 60mph (as compared with 10 - 40mph for same-way cycling). Note that bicycle helmets are only rated for impact speeds of about 12mph. Also, because you're riding against traffic, the number of interactions with other vehicles is greatly increased. Finally, at intersections, drivers entering and leaving the roadway are focused on vehicles coming from the opposite direction and are much less likely to see you.
Statistics show that riding against traffic is at least 3 times (some studies suggest as high as 12 times) more dangerous than riding with traffic, and collisions with 'wrong-way' riders are more often fatal than most other collision types.
In short, the most effective way to commit suicide on a bicycle is to ride against traffic.