The Library of Congress has an enormous collection of primary sources on a range of topics, most related to United States history, but they have some global collections too. Consider browsing their digital collections to see if you can find a topic that interests you.
The Digital Public Library of America gives you access to over 29 million images, texts, videos and sounds across the United States. You can browse by topic, check out online exhibitions, or check out their primary source sets.
University of California San Diego has a great guide full of links to digital archives and other primary sources on a range of topics.
Northern Ireland peace process digital archives - https://digital.library.nuigalway.ie/
Pentecostalism digital archives - http://digitallibrary.usc.edu/cdm/landingpage/collection/p15799coll14
Villanova University’s Catholica collection - This collection makes available digital content of Catholic materials including books, journals, papers, and manuscripts dealing with the Roman Catholic Church in general, and in particular works created or published in the Americas.
International Mission Photography Archive - historical images from Protestant and Catholic missionary collections in Britain, Norway, Germany and the United States. The photographs, which range in time from the middle of the nineteenth to the middle of the twentieth century, offer a visual record of missionary activities and experiences in Africa, China, Madagascar, India, Papua-New Guinea and the Caribbean.
Association of Religion Data Archives (ARDA) - a data collection center on domestic and international religious groups