It is not common. However, there are some exceptions. It is the case of the EB-5 visa for investors, a.k.a. EB-2 NIW. 
EB-2 NIW?
NIW means National Interest Waiver. It is very similar to an EB-2 visa, but it has some peculiarities.
This is a way to get the unsponsored Green Card, which means that immigrants can apply for it by themselves, and do not need the presence of a relative in the United States, nor a request from a company.
Who Can Apply?
Professionals with a master or a doctorate degree. Also, those who have a bachelor degree and can prove five-year work experience in their field.
Foreign entrepreneurs and professionals with extraordinary or above average skills may apply, too. In this case, they must submit the following documents:
- Diploma or certificate from a university or an institution.
- Letters in which work experience is documented (ten years minimum) in the area of specialization.
- Membership in professional associations.
- License to work in that profession.
- Receipt of wages.
- Recognition by colleagues or institutions for professional achievements or contributions to the field of specialization.
- Any other pieces of evidence of professional exceptionality.
National Interest in the EB-2 NIW
All those activities that benefit the U.S. economy, its cultural and educational purposes or its general welfare are considered of national interest.
In the case of entrepreneurs, the USCIS has made clear that job opportunities and direct or indirect economic growth imply the fulfillment of the national interests.
If You Are Not Able to Meet the Requirements…
You cannot sponsor yourself to get a Green Card. However, it is still possible to obtain one, provided that you have been offered a job or an American company is willing to sponsor a simple EB-2 visa for you.