There are a number of digital archives around the world that are free and open to the public and therefore, available to students. This past November, the British Library digitized 800 medieval manuscripts. These are accessible at the British Library.
The Library of Congress has thousands of items that have been digitized and made available online to the public. It houses anything from Presidential letters to to Civil War Maps to notated sheet music, famous and not so famous photographs, newspapers, and legislation.
The World Digital Library is a project of the U.S. Library of Congress, carried out with support of the United Nations Educational, Cultural and Scientific Organization (UNESCO), and in cooperation with libraries, archives, museums, educational institutions, and international organizations from around the world.
The WDL makes available on the Internet, free of charge and in multilingual format, significant primary materials from all countries and cultures including, Chinese rare books, Mozart’s original manuscript score of the Magic Flute, works by Galileo Galilei, primary documents from US history, and more!
The Library and Archives of Canada has archives and digital collections which include governmental records, immigration records, photographs and a collection on indigenous heritage.
The National Library of Australia has a few digital collections accessible from its home page. This includes Trove, a group of collections from hundreds of Australian cultural organizations.
The National Archives of Australia also has a number of digital collections available to view.