There are two primary schools of thought when it comes to the creation of corporations in EVE, and each has both good points and drawbacks.
The most popular school of thought is that of a specialization corporation. These are corporations that focus solely on one aspect of the game. Mining corporations are fairly popular, as are manufacturing corporations. The most popular and prevalent by far are the PVP corps. Each of these type of corps focuses on one area of the game and runs with it. By specializing the corporation can market itself to Alliances and quickly make a niche for themselves.
The other school of thought is that of a balanced corporation. These are corporations that cover a majority of the aspects of the game equally. Corporations like this tend to have several components to them - internal divisions that handle the various aspects of the game. Corporations like this tend to take on a more integrated approach and can often support more members.
Now, there are also downsides to both. The specialist corporation tends to have to spend more money on aspects that are not in their sphere - for example, a mining corporation often has to pay for military protection. PVP corporations have to pay other corps for the ships they use. As to the balanced corporations, they don't see as much cash flow as the specialist corporations do because their manpower is split in focus. It also results in each component of the corporation being weaker than an equivilent specialist corporation.
There are real world historical precedents for both. The specialist corporation has existed in the world for quite a bit of time, going as far back as the Industrial Revolution and prior. The East India Company was primarily a shipping and trading company founded in 1600 whose specialty was in trade. During the booming Industrial Revolution corporations sprung up that focused on manufacturing or on industry, utilizing the latest and greatest inventions of the day to help them. Even now, in modern times here on Earth, there are businesses who specialize in one single segment of industry. These range from tool and dye makers to machine shops.
The balanced corporation was a concept that didn't really take off until Andrew Carnegie came to found Carnegie Steel in the mid-1870s in the US. He is considered the founder of "vertical integration" (another term for a balanced corporation), where a company would handle all aspects of it's trade. Another example of this was the Ford Company - though in a different way, for Ford purchased other subsidiary companies. Vertically integrated companies exist in the real world to this day - oil companies are great examples of this as they both drill the oil, ship it, refine it, and then sell it on the market at stations they own.
When I formed The Corporation, I thought long and hard about what I wanted to do with it. I'm a very teamwork-oriented guy and part of a community of like-minded individuals, so whatever we decided to do would have to be teamwork-oriented and teamwork-based. One of the great things that drew me to EVE was the fact that you could do just about anything you wanted - you weren't limited in scope to one class or another. Vertically integrated companies would give me a greater range of talent and give me a greater base of players to build the corporation on. While I liked the allure of being a niche player, in the end I felt that teamwork could be better achieved if there were several elements to the corporation.
So saying, I created the corporation using five key divisions: Mining, Manufacturing, Business, Military, and Science. These were the five major areas of the game that I had identified as bieng key components. Each division has a director, who oversees their division's work and checks in with me and the other division directors.
Now, there are certainly drawbacks to this layout. It takes a bit longer to do non-essential items because all the directors have to be on the same page. Given the nature of real life, not all directors can be on all the time. This was remedied by having Assistant Directors (but it also makes another layer of work). Still, it's been three months and so far things haven't fallen apart, so it looks like the corporate layout is working so far.