The design of a site is as important as everything else, it is what can sell your product. If you have a site which is very unique, looks good and is simple to use then your site is almost guaranteed to succeed. The design of a site can and should vary depending on what the site is trying to do. An e-commerce site should look commercial and be driven by selling your products. A site providing information and advising people should instantly give you the impression of being trustworthy and the source of information. There are many different types of websites each with their own agenda, look and feel.
If you are looking for a site to resemble your personality then it is easier to break the mould of traditional sites. A good example of a different site is JK Rowlings site which draws viewers in. The site is built so you have to explore the site and work out what does what, there are hidden sections which lead to extra sections, this means that the user has fun trying to explore the site rather than just reading information about JK.
There are lots of things to consider when designing a site. Are there colours which make it hard to see text? (not all screens produce the same colour) Have I got my main content in the prime hot-spots on the page? Is my main content at the top of the site so people don't have to scroll to see it? What screen resolution should my site be designed for? Should my site be fixed of flex (stretch when the window is a different size / resized)