There were one hundred and two passengers who arrived at Plymouth on the Mayflower in 1620. Many of those passengers were religious pilgrims from the Leiden congregation; some came for financial gain and to acquire land; and about twenty were sailors manning the ship. About half of those people died during the first winter at Plymouth Colony. Today, tens of millions of Americans claim these original pilgrims as their ancestors. Those who can document their claims are eligible for membership in groups like the Mayflower Society.
The Mayflower Society, or the General Society of Mayflower Descendants, was founded in 1897 by pilgrim descendants. It is the oldest and the most prominent Mayflower genealogical group. Both religious and non-religious Mayflower immigrants are considered "pilgrims" by the society, and their descendants are eligible for membership. For membership requirements, go to: http://www.themayflowersociety.com/index.htm.
Since the pilgrims were a well-known immigrant group, many people today try to fraudulently claim Mayflower descendancy. Beware of websites and published books that don't have documented sources; you don't want to corrupt your family tree by accepting someone else's fake claims as fact. But if you want to find out whether or not your ancestor's Mayflower claims are true, there are reliable sources that you can search.
One good resource is Plymouth Massachusetts History and Genealogy, which has published online a list of all Mayflower pilgrims at:
http://www.usgennet.org/usa/ma/county/plymouth/passengers.htm. You can click on each individual to view his or her spouse, children, birth information, death information, biography, and ancestry.
Another good website is the Plymouth Colony Archive Project at http://www.histarch.uiuc.edu/plymouth/index.html. This archive has fully searchable texts for the early years of Plymouth Colony, including journals, court records, probate inventories, and wills. On the archive project's site, you can search by the name of the ancestor you're looking for. Don't forget the New England Historic Genealogical Society at http://www.newenglandancestors.org/default.asp. Founded in 1845, the society is the oldest and most respected group of its kind in the United States. And, not surprisingly, its collection for Mayflower passengers is almost unrivaled. All these resources can help you learn more about your connection to these brave early colonists.