In our 8 February show, we answered an email regarding how to determine the popularity of one's surname. Of course, there are many aspects to such a question, but we mentioned a couple of web sites that provide some statistical studies of a surname's frequency in a given population. The most popular of such lists is from the U.S. Census Bureau, which has tabulated the data from the 1990 census. That information is best approached on their Frequently Occurring names page, where both surnames and given names (male and female) are available to be searched. Be sure to review their methodology page to understand the limitations of that data.
Wikipedia has a list of most common surnames for many different countries, drawn from various sources. For the U.S., they used the census bureau's above site. The same census data is used for the tables at MongaBay.com. An interesting site at RoyAshbrook.com apparently uses the Social Security Death Index to tell what rank a surname has in popularity. It does not generate a list of most popular surnames, but rather reveals a name's rank when typed into the box.
However, the frequency of a surname will vary over time. Hence, researchers may also want to use large databases, such as census indexes, to determine the relative frequency of a name in a specific place and time. For example, a database such as the SSDI would reflect the frequency of a surname in the first half of the 20th century better than earlier or later time periods.
As an illustration, consider the surname "Young." In the 1790 U.S. census, this name ranks 13th in frequency. The RoyAsbruck site places it 29th, while the 1990 census lists Young in 28th place. It appears that the addition of more non-British surnames to the U.S. population in the last 200 years has diminished the frequency of Young, and perhaps many other surnames.
One other problem with such lists is that they generally don't combine similar spellings: Young and Younge (44,828 in 1990), and should Younger and Youngers also be combined with Young?
For a different, but related take on surnames in the U.S., see Hamrick Software's surname maps that show the relative distribution of a surname in the U.S. population in 1850, 1880, 1920 and 1990.
Ancestry provides similar maps showing specific numbers of families with any surname in 1840, 1880 and 1920 in their free Family Facts page. For more sites, try searching Google for surname distribution or surname popularity. Have fun!