Prior to the almost universal ownership of telephones, most large cities, and some not so large, compiled city directories that included an alphabetical listing of residents. Most of these directories included addresses and sometimes even the person's occupation. Many included the person's marital status as well. If you are lucky enough to find sequential directories between census years, you may be able to tell the approximate year an ancestor died which will speed your search for death records. Other information in some directories were the names of adult children still living in the household.
If you've had trouble locating a family on a particular census, the street address in the city directory can help you track down the proper census roll you need to peruse. Occasionally, these directories will also include a reverse index --- a listing of streets with the names of all people living on that street. This can be an invaluable tool in locating other family members or even surnames that married into the line you are researching.
Directories also often specify whether the person named was an owner, renter, or boarder. If your ancestor was listed as an owner, that means land and/or deed records should also be available.
It is also a good idea to check out the churches that are located near where your ancestor lived. If you know the denomination of the church they attended, one of those nearby may have records pertaining to your family. If you don't know the denomination, but you have a marriage license with the name of a minister officiating, check out the address for this minister and see which church it leads to.
As in any transcribed list, there may be omissions or typographical errors. Be sure to check all variations of spelling for your surname. In some instances, entire neighborhoods were left out of the directories, usually based on ethnicity or working class.
Most local libraries maintain old city directories and there are extensive microfilm copies for those of larger cities. If your library doesn't contain the directories you need, check out one of the sources below and see if you can either obtain an intra-library loan, or arrange for someone to search the directory for you. Be prepared to pay a fee for that service.
Allen County Public Library, Fort Wayne, Indiana
Allen County Public Library
American Antiquarian Society, Worcester, Massachusetts
DAR Library, Washington, D.C.
National Society of the Daughters of the American Revolution Home
Family History Library, Salt Lake City, Utah
Library of Congress, Washington, D.C.
Library of Congress/digital collections/historical newspapers - FREE
New England Historic Genealogical Society, Boston, Massachusetts
New York Public Library, New York City, New York
New York Public Library