This is one of the few occasions where I'd disagree with Val. I'd say that third party liability is ESSENTIAL. I recently went to one of the excellent Dog Law Seminars (see the DogLaw website for more info). Not only would I recommend the seminar wholeheartedly, but it also confirmed the importance of insurance, so much so that as soon as we got home, I nagged/persuaded DH to check our policy cover.
We live in a very litigious age, rightly or wrongly. Let's picture a few scenarios. Your dog is off lead in the park, and trips up a cyclist or runner. They break a bone. Before you know it, you're paying out for medical costs, possibly physio, loss of earnings, their legal fees, your legal fees and a whole host of things I probably haven't even thought of. Your dog escapes from the garden and is involved in a car accident. Running on the road, a car driver slams on their brakes to avoid him, and gets shunted from behind. Now we're talking telephone numbers because cars are involved, and the driver claims for whiplash and so needs to visit a chiropractor at £40 a session, plus those legal fees, and and .... you get the picture. Also, if in the very unlikely event your otherwise perfect dog does bite someone (even if provoked by a child who thinks it's OK to "torment" dogs) wouldn't you want the best legal advice and behavioural support that you could afford?
I honestly do think that making sure you have this form of insurance is essential, along with good solid veterinary cover. The two together won't cover all eventualities but will ensure you can take problems in your stride, as even the most responsible owner and the best trained dog can have unexpected incidents and events.