All websites should have some sort of tracking software installed, whether it be Google analytics or server side installed packages. The best option is to install both as some stats software does not show certain elements that the other one might. Being able to track results from people visiting your site is a great tool for future marketing and improvements.
With mist software you can see how people found you, which pages they visited and how long they stayed on certain pages. As well as that, many of them now allow you to also follow a visitor through your site and see the path they took and if they completed a certain action e.g. filling in a contact form. Studying web statistics can help you prioritise where you should be spending your marketing budget and show you which elements of the website works and which do not.