Between the fifth and eleventh centuries most people were illiterate and lived in rural areas or small villages. They were known by their first names and perhaps the place where they lived. As populations grew surnames were needed.
A list of the most common surnames for many countries is located in the wikipedia:
http://en.wikipedia.org/wiki/List_of_most_common_surnames
A search for surnames for individual countries in Google also produces several sites to browse.
According to the 2000 U.S. Census, the top 100 surnames are as follows:
http://en.wikipedia.org/wiki/List_of_most_common_surnames#United_States
There are four main categories of surnames. Most surnames are derived from the father's given name such as Johnson or Thomasson. Some come from geographic names such as Meadow, Hill, or Atwater. Other names come from a persons occupation such as Smith or Carpenter. Descriptive names include Long, Armstrong, Blake, and Stern.
The Lake County Public Library has many books to help genealogists with surname research. Look under the call number 929.4 for more interesting information about the origin and history of surnames.