According to the IRS, there are five types of business entities: Sole Proprietorships, Partnerships, Corporations, S Corporations, and Limited Liability Companies. Many state statutes allow for additional entities, such as Limited Liability Partnerships and L3Cs (You can register in Colorado as the former, not the latter). For the majority of entrepreneurs, the only real choices are the LLC, the Corporation, and the S Corporation.
I don’t think it makes sense for most business owners to choose Sole Proprietorships or Partnerships today. With the freedom and simplicity with which you can form a Corporation or a Limited Liability Company, it makes sense for almost all businesses to formalize their business process enough to obtain limited liability protection. In Colorado, it costs $50 to form a corporation or a limited liability company. This means, in essence, that the Secretary of State allows you to purchase insurance to protect all of your personal assets against liability associated with your business activities in exchange for a one-time premium of $50. That’s just too good of a deal to pass up.
If you decide not to organize your business, by default, you are a sole proprietor. If you decide not to organize your business and you are working with a partner, you have formed a partnership. By accepting these defaults entities rather than forming an LLC or a corporation, you are subject to the default laws of the state. In most states, it doesn’t matter if you do 90% of the work and your partner does 10%, absent a written agreement to the contrary, you’re 50-50 partners.