Thanks to Greg Barber, MLC Greens for some raw data research, I've prepared these charts of trips and accidents in Melbourne. The first graph is for the City of Melbourne (trips measured by destination). The second chart is for Greater Melbourne. In both charts the number of trips has been divided by the average ratio of trips to accidents, to make the comparison easier. The census trips to work is measured every 5 years, as you can see it outpaces the number of accidents (reported). Many things could be causing this, including generally safer conditions on the roads, e.g. pedestrian accidents might be decreasing also. It could also be due to increased numbers cycling, or better bike lanes and cycle paths.
The general idea is that the more people cycle, the safer it gets for everybody. This could be because motor vehicle drivers get more used to seeing bicycles, or because attitudes to cyclists change when it is more common (a car driver probably knows more people who ride, for example).
Countries with the most cycling (Holland, Denmark, Sweden, Germany) are also the safest. This does not establish cause and effect but it is suggestive. It could also be argued that because those places are safer to cycle, therefore more people do it. Either way, safety and greater numbers are both objectives that need to be achieved. These are also countries without mandatory helmet laws.
Safety in Numbers is also the reason why high quality bicycle lanes will increase safety, mainly because they increase the number of cyclists on the roads generally.
A problem for transforming places like Melbourne, USA and UK into cycling cities is that the established cyclists who are used to "vehicular cycling" (i.e. toughing it out with the motor vehicles) are not receptive to segregated facilities. In the UK the main cycling organisations are locked into this disasterous policy mistake. Fortunately in Melbourne, Bicycle Victoria understands cycling much better and advocates for high quality infrastructure.
See cyclehelmets.org on Safety in Numbers.
Some references from the Cycle Promotion Fund's paper on the Health Benefits of Cycling:
Jacobsen, P.L., Safety in numbers: more walkers and bicyclists, safer walking and bicycling, Injury Prevention, 2003, 9 :p. 205–209,
Robinson D.L., Safety in numbers in Australia: more walkers and bicyclists, safer walking and bicycling, Heath Promotion Journal of Australia, 2005, Vol 16,
Issue 1, pp. 47-51,