No matter how careful you are, it's impossible to guard against everything that could possibly happen to you. To protect yourself against a lawsuit, you need to have insurance that protects you from third-party liability.
Third-party liability coverage can be included as part of a range of insurance types including vehicle, business and homeowner coverage. In an auto policy, the third party could be the person suing you because you rear-ended their car or the person whose fence you destroyed when you swerved off the road. With a homeowner's policy, the third person could be the friend (or former friend) suing you after your beloved puppy bit her. If you own your own business, third-party liability coverage could kick in if a customer is injured while using your product.