Yes, many of my ancestors did vote - or at least registered for the privilege, and these official records can often be a valuable source of information for genealogists. If nothing else, voter registration records provide an address where your ancestor was living during the gaps between census records, but you may also find naturalization information, voting records, or your ancestor's signature. You can also learn more about your ancestors by checking the voter laws in effect at the time in that area - many places enforced a residency requirement of a certain period before allowing an individual to become a registered voter.
In the southern United States, the 1867 registration of voters was the first to enumerate the recently emancipated black citizens, as well as men who had survived the Civil War. This particular registration is especially helpful for genealogists, because many Southern families -- both black and white -- relocated during the period between the Civil War and the 1870 Federal Census. Many of the extant 1867 voter registration records, which include names of voters who registered to vote between 1867 and 1869, can be found at the state archives, or on microfilm from The Family History Library. There are also some examples of these valuable records online such as Alabama 1867 Voter Registration Database from the Alabama Department of Archives & History.
In August 1920, ratification of the 19th Amendment first gave women in the United States the right to vote, making that year's voter registration records a great place to begin the search for your female ancestors who were U.S. citizens at the time.
The United States, of course, is not the only country with voter registration records. Freeholders' Records in Ireland are an especially valuable resource for genealogists due to the scarcity of Irish documents available for the 18th and early 19th centuries. The Public Record Office of Northern Ireland has digitized about 5,500 sheets from pre-1840 Irish Registers and Poll Books, and offers them online for free accompanied by a searchable name index. The Canadian Genealogy Centre offers an excellent online article concerning the many voters lists available in their collections and how to access them. Similar voter lists and electoral rolls exist for England, Australia, France and other countries around the world.
Other significant online collections of historic Voter Registration rolls include:
The majority of voter registration records will not be found online, but that does not mean that they don't exist! Check with the local historical society, or the state archives or library (most offer online catalogs of their holdings) to see what voter registration records exist for your area of interest and where they might be located. A good example of the type of information you may find online is this finding aid for Woodbridge, Connecticut Voter Registration Records. The Mormon Family History Library has also filmed many voter registration records for areas around the world. Search the Family History Library Catalog online to see what's available -- some of them are even available online, such as Jackson County, Missouri, Voter Registration Records, 1928-1956.
It might go without saying, but remember that if your ancestors were not citizens of the country in which they lived, then they won't be found on voter registration records! Many immigrants, including my paternal great-grandparents, never found the right to vote enough of a reason to become naturalized citizens.