About 10% of Americans are descended from someone who was brought to the shores of Massachusetts in the winter of 1620 on the Mayflower.
When you consider that there were originally only 102 passengers, and that about half of them would die that first winter, that's pretty astounding.
MayflowerHistory.com is a fantastic resource for Mayflower history and genealogy, and, among many other things, it has a transcribed passenger list, with individual passengers' names hyperlinked so that you can learn more about them. There is also pdf link to an image of the original list made by the hand of Governor William Bradford in 1651.
Some of the more common/prolific Mayflower passenger surnames are Alden, Billington, Bradford, Brewster, Chilton, Eaton, Fuller, Hopkins, Howland, Standish, and Winslow. If you have these names in your family tree (or any others on the passenger list), you might want to dig back further on those lines.And since the Mayflower passengers married into each other's families, chances are that, if you have one Mayflower ancestor, you probably have others.