Harvard University's Open Collections Program is a project that allows the public to access, via the internet, thousands of resources held in the Harvard libraries. The Open Collections Program's website on Immigration to the United States is a treasure trove of primary sources on American immigration history.
The Library of Congress has put together an excellent website for students and teachers interested in the history of American immigration. The site, which includes many fascinating primary sources, is organized by ethnicity.
The Online Museum of the City of San Francisco contains a wealth of material dealing with the Chinese presence in California in the nineteenth century, and the nativist backlash against it.
The Cork Multitext Project, a project of University College Cork in Ireland, has built a fantastic website on the tragic history of the Great Irish Famine and its consequences, which include mass emigration to the United States.
The United States Census is the best source of raw data on immigration (and many other topics in United States history). Here the Census Bureau presents a table detailing the nationality of the country's foreign-born population since 1850.