You would be surprised how many people come to me to discuss a redesign and tell me they do not have a contract with their existing developer. It baffles me how this happens. As a developer I have a standard contract that I insist the client signs before we begin work. This is to protect them just as much as it is to protect me. I do not know any good developer who doesn't insist on a signed contract. If you are in negotiations with a developer at the moment and they don't require a contract I would question why? Will you own the website at the end of completion?
If you don't have a contract then you have no standing over the files of your website. You need to make sure that on completion you get a full back up of the site to keep safe as well any database and images.
You would get a contract for any other major purchase in your life – like a car, etc so why wouldn't you want one for a major purchase like a website. The website is going to be a major part of your business so make sure you are in control.