You can get a family based green card so long as you are an immediate relative of a U.S. citizen. Who is an immediate relative? Husband/wife, (even if deceased but the death must not have occurred more than 2 years prior); unmarried children under the age of 21 who has at least one parent who is a U.S. citizen or greencard holder; parents of a U.S. citizen child over 21; step parents if the marriage occured prior to the 18th birthday of the petitioning child.
You can get a family based green card if you are a "preference relative" of a U.S. citizen or a greencard holder. Who is a preference relative? There are four categories.
Family First Preference
Family Second Preference
Family Third preference
Family fourth preference.
You can also get a greencard if you are an accompanying relative of someone in a preference category.
So in short, there are three ways by which to qualify for a family based greencard.