The Library of Virginia, Virginia Historical Society, and University of Virginia have large collections of newspapers for the state.
Indexed images of the Virginia Gazette (1736-1780) are available online through the Colonial Williamsburg website. In addition, Professor Tom Costa and The Rector and Visitors of the University of Virginia have created a database of all runaway advertisements for slaves, indentured servants, transported convicts, and ship deserters listed in this source and other Virginia newspapers (1736-1803), see: The Geography of Slavery in Virginia. These newspapers are valuable resources for all regions of Virginia.
The Family History Library has acquired very few copies of newspapers from Virginia. A bibliography of Virginia newspapers is:
Cappon, Lester J. Virginia Newspapers 1821-1935: A Bibliography with Historical Introduction and Notes. New York, NY: D. Appleton Century, 1936. (Family History Library book 975.5 B33c; fiche 6104102.)
Earlier newspapers are discussed in:
Brigham, Clarence Saunders. History and Bibliography of American Newspapers, 1690-1820. Two Volumes. Worcester, Massachusetts: American Antiquarian Society, 1947, 1975. (Family History Library book 973 A3bc.)
The Family History Library has copies of some published indexes of newspapers, such as:
Cappon, Lester J. and Stella F. Duff. Virginia Gazette, Index 1736-1780. Williamsburg, Virginia: Institute of Early American History and Culture, 1950. (Family History Library book 975.54252 B32c; film 1036212 items 2-3; fiche 6051225. The newspapers for these years are on Family History Library films 029718-23.)
Hall, Virginius Cornick. Abstracts of Marriage and Obituary Notices in Virginia Newspapers Before 1820. Salt Lake City, Utah: Genealogical Society of Utah, 1987. (On four Family History Library films 1508537 and 1508567-69.)
The Library of Virginia has indexes to obituaries and marriage notices printed in the Richmond Whig and the Richmond Enquirer from 1804 to 1857. Some of this information has also been published in:
McIlwaine, H.R. Index to Obituary Notices in the Richmond Enquirer from May 9, 1804 through 1828, and the Richmond Whig from January 1824 to 1838. 1921. Reprint, Baltimore, Maryland: Genealogical Publishing, 1974. (Family History Library book 975.5 A1 no. 52; film 908702 item 6.)