I've cycled to work on-and-off for over 10 years, and I've never had a serious accident. I've come off the bike twice in all that time. On each occasion it was entirely my own fault. I cycled off a high kerb on a pitch-black night in an unlit park. The other time I was riding too close to the back of a London bus, then, when it braked, I cut out right only to find a stationary car in lane 2. Oops. On both occasions I escaped with nothing more than a bruise or two.
A couple of scrapes is nothing in 10 years. Perhaps that's why it was a shock to hear that three London cyclists have died already in 2010, in collisions with Heavy Goods Vehicles. The great Real Cycling blog provides stats, links, and some perspective.