|Molly Pitcher, famous Revolutionary War gal|
The Daughters of the American Revolution -- the venerable D.A.R -- has one of the most comprehensive and well-respected collections of genealogical resources in the United States.
Just about all of it is hard-copy or microfilm, meaning you'll have to visit the main DAR library in Washington, DC to take full advantage of their resources.
However...there are two free, online resources from the DAR that you should definitely take a look at.
The first is the DAR Online Library Catalog. A search here on an exact name or surname will quickly show any library holdings that are by, or about, the name in question. If you're familiar with my Bourne Test, I turned up 50 Bourne's in the catalog.
Just as easy to search, but a seemingly much larger dataset, is that of the GRC -- the Genealogical Records Committee of the DAR. There are more than 35 million names recorded here, including 785 Bourne's in New York, alone (and thousands in the US, though the search results max out at 1,000).
From what I can tell, other libraries (such as FamilySearch.org) have copies of the GRC records, but do not have the full index that is available at the DAR GRC lookup page.
The DAR library also has special collections devoted to African-American, Native American, and Jewish family history resources. Might be worth a visit, if your heritage lies along those lines.
Don't forget to also check for your family history at NewspaperArchive and Newspapers.com. These are subscription databases, but they are among the most powerful research tools available for looking into family roots. And visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.