I think the safety record for cranes in terms of them actually falling over is relatively good. The danger of a falling crane affects surrounding workmen and members of the public, who are more likely to be injured or killed than the crane driver, in the event of a fall. For the driver, the most dangerous part of the job must be climbing to and from the cab, which presents a potential falling hazard, but for the driver, rather than the crane itself.
I actually work advising people on training for Construction Plant, which covers cranes. The accident rate gets lower and lower. Training is now high priority and Health and Safety is an extremely important part of it. The construction industry is hoping for more women to train in driving plant and machinery on sites. Were you considering this Aimee. If so, I'll point you to a good website.