Redesigning your website not only gives you a chance to update its look, but also to update its functionality. Starting a new project for your website allows you to reevaluate its purpose, reorganize its content, and make any fundamental updates you just haven't gotten around to.
Upgrade its usability
The point of a having a website is to have people use it. Good content is a start, but with the web expanding daily, chances are that text isn't the only thing you need going for your site. If you have an outside service you rely on to interact with users, think about fully integrating that into the site. Having an on-site blog, calendar, various forms, documents, etc. that are accessible from your site helps ensure your users will never have to leave it to get what they want.
Integrate a new look
Your website's look-and-feel may have been cutting edge when it was first designed, but it's been years now. Years don't mean much in "real life," but in internet time, it might as well have been decades. It's time for an update. If your site looks out of date, users might not trust you to have up to date content and resources. Updating your functionality and your design at the same time saves you the trouble of trying to integrate new technologies into old ones. Think square peg in a round hole: you'll need a mallet and something has to break.
Plan it out
It's your site, of course you know where everything is. Do your users? Since you're reorganizing your content, it's a good idea to make sure all the information you want to be known for is at the forefront of your site, instead of being buried under endless navigation. See: How to Organize and Plan Website Content.
Increase its value
Your website is an affordable way to promote yourself, organize resources for yourself and users, and interact with existing customers and grow new ones. All for a small hosting fee. Updating an existing site is an easy way to increase the overall worth of your online presence.
Your website is often the first thing a customer will see about you and your company. What message are you saying with it?