An atlas and/or gazetteer is an essential tool for the genealogist. Let Rand-McNally be your friend.
County boundaries have changed often over the years. Counties sometimes get split into two or more counties. Some get abolished or renamed. See the book Map Guide to the U.S. Federal Censuses of 1790 - 1920 by William Thorndale and William Dollarhide, published in 1992 by the Genealogical Publishing Co. of Baltimore, $40.
U.S. Geological Survey (USGS, part of the Department of Interior) maps and data are helpful. See their web site at www.usgs.gov/pubprod for what is available from them.
Township names are often given instead of town names. Many libraries will have a book showing all township boundaries. One book is Township Atlas of the U.S. by John I. Adriot, 1979, 1991, McLean, VA, Andriot Associates Publications, over 1500 pages. The Library of Congress Number is OCM24340903. The call number at Mid-Continent Public Library is 912.1 AN28A 1991
Side note: townships are six square miles in size. Thomas Jefferson came up with the idea.
Note that both of these files are self-extracting zip files. To unzip them, double-click on their name within Windows Explorer and save them to wherever you wish. The self-extracting file for the U.S. places is pretty self-evident, three columns of data: state, county and town. The self-extracting file for the English places has a small companion file that explains the format/layout of the records. To view either of these files, they can be opened in a text editor, such as Notepad, or in a word processor.