Recently I had to resurrect some of my high traffic sites after they were down for a few weeks due to hosting trouble. I was pleasantly surprised to find that they still had some traffic coming to them and I started earning immediately. This made me realise how valuable the domain name of a successful website is:
All the backlinks point to the domain name: All the links to your site from other sites point to your domain name not to your hosting provider. Ideally this means that your websites are hosting independent and can be moved from one host to another without losing any traffic.
People remember your domain name: On some of my sites I get a lot of type in traffic. My visitors remember my site’s domain name and directly visit it. This sort of traffic is usually the most valuable because these users are interested in your site and are motivated enough to remember its address. Since they are interested in your site they will also be interested in relevant ads that are there and click on them earning you money.
Because of these two reasons it is often considered best to purchase your domain names from someone other than your hosting provider. This ensures that if your hosting provider turns out to be troublesome you at least have access to your domains and can switch hosting providers.