Even if the answer of this question is something really obvious to most of us, I will try answering it with an unusual way, comparing web design business with cell phone industry.
This question it’s similar to the one that you might asked 15 years ago. “Why do I need a cell phone?” The answer is simple, 20 years ago 5% of your friends, family or colleagues might had a cell phone.  What was the point of having a cell phone when 95% of the people around you didn't use it? Now 95% of these people have cell phones, so obviously if you want to reach them or if they want to find you, you need one too.

Another important factor was the price and the technology. 20 years ago a cell phone with so little features costs 1000 euro and most of people found it unnecessary due to the high price and early technology issues.

Now imagine the same scenario considering the Internet. Around 15 years ago 5% of the companies or entrepreneurs had websites, and 5% of people where using the Web.  So again, having a website, despite the fact that it would have cost you a fortune to do and it would have been with so little features, that website would not be enough to satisfy your needs. There was no point to spend so much money considering the fact that there were so little people to use it.

Comparing the above two scenarios with the facts today, it is obvious that you cannot live without a cell-phone and you cannot exist in the Internet without a website. You need a website because it’s what makes you part of the game in the Web.  Your website domain name it is your representative ID in order to be found in the Internet, same as your cell phone number, which is your representative ID in the telephone network. People call your number to reach you; they also hit your name in Google to find you in the Web. In addition web design and cell phone industry is now 10 times cheaper and better than 15 years ago.

And now the exciting part… Have you been in a cell phone store lately or did you find yourself trying to choose a cell phone among hundreds of mobile/smart phones? Are you confused at what is best for you? Android, Windows phone, I-phone, Blackberry? Have you been shocked of the amount of applications that are available?

Be prepared to do the same and much more questions to yourself, when you will have to decide about the website of your business.