In reply to tom.dodo: It's "all fun and carefree" right up to the point where YOU cause an accident which leaves someone else with a life-changing injury, or even dead. Then they, or their next of kin, will be seeking compensation, not to punish you but because they need it to maintain some quality of life.
Don't think that you won't get sued "because we all accept the risks" or "it's not in the spirit of the sport". Romantic ideas about the partnership of the rope may not stand up for long against the prospect of being unable to work again, and a life on benefits. The person you injure may not be your mate but a total stranger, perhaps just a passer-by and not even a climber, who will have no qualms about suing you. Or it might be their widow, who's unlikely to be sympathetic to that argument either. Perhaps they've claimed on their own life or accident insurance, which means their insurance company will be after you to recoup what they've had to pay out.
There's a useful paper on the BMC website which explains the different types of liability and insurance cover available. Like so much on the new-look website, it's not easy to find and its tucked away amongst the club guidance - not an obvious place to look if you're not in a club.
Just because someone gets injured doesn't mean someone can be sued. For 3rd party liability to arise you have to be negligent in the legal sense, which is more than just ordinary carelessness. 3rd party insurance exists to protect the victims of your negligence. If you have assets, it protects you against losing them. Even if you don't, you at least have a moral obligation towards those you might injure.
It should be a no-brainer. Let's face it, this is dangerous activity, accidents happen, and sometimes someone is to blame. Don't think it couldn't be you, or couldn't happen to you. You should have 3rd party cover, and you should consider accident insurance for yourself, in case YOU get injured and it's not due to someone else's negligence (or they're not insured). You should also make sure the people you climb with have insurance too. This is one of the benefits of belonging to a BMC-affiliated club - you know that that any members you climb with are automatically covered. If you don't want to join a club, become an individual member and get personal accident cover too.