Family and employment green cards have waiting lists. The waiting times vary depending on the country from which the applicant is immigrating due to country-specific caps. According to Stephen Yale-Loehr, an expert on immigration law at Cornell Law School, U.S. Citizenship and Immigration Services is currently processing green cards for persons who have been waiting for these years (India and Mexico illustrated):

Family based 

Immediate family: spouse, minor child or parent of U.S. citizen, no caps.

First preference (F1) – unmarried sons and daughters, 21 years of age and older, of U.S. citizens.
India May 2011, Mexico August 1997. That is, Indians in this category who applied in May 2011 are now being processed.

Second preference (F2A) – spouses and children (unmarried and under 21 years of age) of lawful permanent residents. India July 2016 Mexico 2016

Employment based

1st preference: Has extraordinary ability in the sciences, arts, education, business or athletics, or Are an outstanding professor or researcher, or Are a multinational manager or executive who meets certain criteria. India January 2012 Mexico May 2016

2nd preference immigrant worker: Is a member of a profession that requires an advanced degree, or Have exceptional ability in the sciences, arts, or business, or Are seeking a national interest waiver. India March 2009 Mexico closed as cap was reached.

Here are the procedures for applying for a green card.