According to its home page, RootsWeb.com is the "oldest and largest FREE genealogy site". RootsWeb hosts a number of sites including Cyndi's List. Since 1996, Cyndi Howells' site has been a good index to genealogical sites on the Web. If you are just starting out, a good first stop would be Cyndi's List: Beginners page.
Another site hosted by RootsWeb is the USGenWeb Project. This is an all volunteer effort which is trying to place genealogical information for every county in the United States on the Web. (For example, see the Harris County page.) Plus, there is a Tombstone Project. Volunteers are needed to walk cemeteries and transcribe tombstone inscriptions.
Major genealogical libraries such as the Clayton Library Center for Genealogical Research (a branch of Houston Public Library) have Web sites as does the Church of Jesus Christ of Latter Day Saints for family searching.
Did great-grandpa or great-grandma perhaps enter the United States through Ellis Island? If so, check out the American Family Immigration History Center.
Not everything is available on the Web yet. Genealogists still spend a lot of time in libraries going through Census records on microfilm. But more and more is available everyday and, if you are interested, more volunteers are always needed!
For more information see: