During their lives, it's common for dogs to develop chronic conditions (allergies, ear infections, diabetes, and arthritis to name just a few). Dogs also get hurt. Everything from broken bones and sprains to soft tissue injuries, snake bites and bee stings. They ingest things that may cause a blockage which can require surgery. If your dog has an ACL injury, that surgery's gonna cost you a pretty penny. Think five figures. And dogs, just like people, can suffer from allergies, dementia, most cancers, diabetes, GI disorders, as well as heart, kidney and liver disease.
A note to all you Lab lovers out there. If you have a Lab for god's sake get health insurance before you bring your puppy home. Labs will literally eat anything they can get in their mouths. The first time I took my current Lab to the vet for a belly ache, he said "let's just go straight to the x-ray". No point in a physical exam. He knew. He has Labs.
There are lots of health insurance policies out there. Here's a link to the a side-by-side comparison of some of them from Consumers Advocate.