From 1790-1840, when the U.S. Federal Census was taken, only the name of the Head of Household was recorded. The number of other people living in the home was also recorded, and the only possible identifying factor is their age at the time of the census, which gives us a range of years between which any given person could have been born.
This chart I made is a useful tool for calculating the range of years the household members were born in. You can also find a handy form to automatically summarize the ages of the household members here.
To find and view free census records online, check my Genealogy Links page.
Tip: If the person was listed under the column for ages 0-9 in 1800, they were born between 1791 and 1800. If on the next census (1810) they were counted under the column for ages 16-26, then they were born between 1785-1794. Since we already know, from the 1800 census, that they were born after 1791, we can estimate the person's birth year was sometime between 1791 and 1794. Other census records may help reduce the range even further, helping you pinpoint the exact year of birth, keeping in mind that some people were mathematically challenged.
UPDATE: TRY TWO OF MY NEW FREE TOOLS!