At Visual Swirl, Leighton Taylor looks ponders how web sites should be designed. They are a tool that can prove relevance, but aren't as important or constant as a logo. At the same time, there should be a usable design and show the personality of the brand.
A great point Taylor brings up is that while the design of great webpages has changed over the years, the great permanent structures stay can be beneficial to a brand. Their examples are Amazon and Apple.