A Limited Liability Company, often called an LLC, is quickly becoming the most popular form of entity to start a business with. It is fairly easy to maintain & mange, yet still separates you from the business, and has the ability to protect you with limited liability.
A corporation is also a very popular and common business entity. It is very flexible, and can have great tax advantages. Because of its structure, a corporation can help shield the business owners, or corporation's shareholders, from personal liability. A corporation, whether S-Corp or C-Corp, is a separate distinct entity under the law.
A Nonprofit Corporation is designed to help nonprofit organizations incorporate. It usually is accompanied by a 501(c) application to apply for tax-exempt status, which helps support the budget of the meaningful cause!
A General Partnership is a simple, easy way to start a business with two or more owners. Although it doesn't have the protection of a Corporation or LLC, It usually only requires registration of its business name by filing a DBA (doing business as). It's important to remember that this business type is not created under the state, and does not separate liabilities from the owners/Partners.
This is the "mom and pop" type of business entity. Many small businesses that run a business themselves start with this type of entity. The legal name is your own name, and it is directly tied to you as an individual. If this is currently your scenario, you can always choose to become a corporation or LLC to protect yourself and your assets.