I'm in the CTC. I've never had to claim and hopefully never will but it gives me piece of mind when cycling past pedestrians and stationary traffic. Its only about £35 which is probably about a tenth of the cost of replacing one of those painted, heated, electricaly adjustable, automatically folding wingmirrors fitted to 90% of new cars nowadays. Imagine if you took out the rear bumper on a new Porsche or something and buckled your wheel so you couldnt ride off! You'd have to leave your bike and do a runner or stay there and stump up for the repair. Or alternatively you could just pop out your CTC card and let them worry about it.
For your 35 notes you get £10million liability cover, 10% off purchases in participating retail oulets (so it can end up paying for itself if your a bit clever) and a free magazine through your door every other month. Its not a bad read either!!!