If you have enough customers, your business is growing rapidly on word-of-mouth advertising and your customers don't use computers, your business does not need a website. If you are working to build your business and brand in an increasingly cyber world, a website is a must.
Whether or not a business needs a website depends a lot on the type of business. If you don’t want a complicated website, look into getting listed in an online directory. That will help your customers find you online.