There are a number of organizations that have legal teams dedicated to providing free legal services on social justice issues, including organizations such as the National Association for the Advancement of Colored People (NAACP), American Civil Liberties Union (ACLU) and the National Center for Lesbian Rights.
Law School Legal Clinics
You can find free legal services at many law school legal clinics that provide free legal services to low income clients by law students under the supervision of an attorney (usually a clinical professor). Generally, this type of pro bono work is offered in one or more particular areas, including family law, elder law, landlord-tenant issues, health care law, and financial assistance. Moreover, law students can provide a range of legal services including, but not limited to, research and writing, drafting legal documents, client interviews, negotiation, and court preparation.