There are many national foundations which offer PhD fellowships. Many of those expect their applicants to have certain political or religious views and/or active social commitment. You can find a summary of organizations recognized by the federal government at www.stipendiumplus.de
International students should search for organizations in their home country. Very often, the government will offer fellowships to graduate in Germany. In addition, you can search the fellowship database of the German Academic Exchange Service (DAAD) for fellowships which will support your stay in Germany.
There are many different sources for a PhD fellowship, but many organizations fund only specific research and/or candidates. We have therefore compiled a short non-exhaustive list just to get you started.