A good point was brought up, contributing to the economy.
When I first started out it was just me, now I have 7 full time employees, but most of the graphic/design work I subcontract out overseas because I just cannot pay what US designers want. I have this constant feeling of obligation to my country to pay an in house designer or sub it out to a US designer but they are all mostly expensive and entitled.
I think this question is kind of silly to begin with but since it is being discussed I will consider it. Even when it was just me, your damn right I considered it a real business. I did not perform good enough, ultimately I would not pay my bills. I don't talk about what I do to most of my friends because they do not understand and usually just say 'web development.'
I also agree with the above of building a brand. In the beginning when I started it out was cute getting a logo and having matching colors etc. but it is much more than that. Building a brand for me is caring about my reputation. A person that works for me is very gung-ho and wanted to "wrap" their car in our brand, and I had to say no due to the fact that I know they are an erratic driver, and tend to frequent establishments that I do not want associated with my brand. I think even 1 year ago I would have given the go ahead to that person and not have considered the situation.
Point being when I really feel like I have a business because I really care about its reputation and how it is perceived locally and on the net.
I am very proud of my business, I live in a section of South Florida where there are a ton of illegitimate businesses such as time share recovery, "ligtht bulb scams (dont ask", metals/commodities rooms, "publication journals", etc so I am very sensitive when it comes to reputation etc.
Kudos to everyone out there that has fulfilled their dreams!