Great responses here. I would simply add that while you need to be keenly aware of the tips provided in these responses, don't be afraid to do a site redesign. Recently we did a site redesign for a new client who had decent rankings and traffic. We 'Wordpressed' their site, keeping all content, images, and the layout basically the same but simply placing it into a Wordpress format. Within a week after the redesign the client's rankings improved in 41 places, according to SEOMoz Ranking. What does this mean? It means that you should not be afraid to go forward with a redesign, because if done correctly you can actually improve your rankings without doing any SEO work.