Some Ohio County birth recordsinformation

Fayette County Births - Carnegie Public Library - Washington Courthouse, Ohio - full transcription of birth records for 1909-1999
http://www.cplwcho.org/birth_search.php

Greene County - Public Library - Birth Records, 1869-1909
http://www.greenelibrary.info/Collections-and-Resources/Birth-Records-1869-1909.html

The Lawrence Register - this independent volunteer website has Lawrence County, Ohio births from newspaper announcements, and extracted from health department and Probate Court records - births range from 1850 to 1940 (formerly at http://lawco.rayhaas.us/births/index/index.htm)
http://www.lawrencecountyohio.com/node/92

The LDS FamilySearch site has images of Toledo, Ohio Roman Catholic Parish Register pages, including baptisms, for 1796 through 2004. Browse only, not indexed. To search newly added records or if link is broken, see the menu for North America at Family Search Beta.
http://pilot.familysearch.org/recordsearch/start.html#p=waypoint&s=waypointsOnly&c=fs%3A1494476&w=0 (requires Flash and Javascript)

Ohio Births and Christenings 1821-1962 - Family Search has indexed about 861,000 birth and christening records, with listings from nearly every county. Recent records may not be available due to privacy laws. Click here for how to purchase copies of indexed records if you need them before they go online. To search newly added records or if link is broken, see the menu for North America at Family Search Beta.
http://pilot.familysearch.org/recordsearch/start.html#c=fs%3A1680845&p=collectionDetails

Genealogy Trails has user submitted transcriptions of birth and baptism lists and announcements for many Ohio counties, from as early as 1821 up to 1980. Note some birth entries are extracted from obituaries and other death records. You may want to modify this Google site search to ease your search, or browse for new entries starting from the Ohio page at:
http://www.genealogytrails.com/ohio/

Rootsweb's User Contributed Early Birth Records Databases include selected births from Butler, Clermont, Columbiana, Coshocton, Franklin, Jefferson, Lawrence, Lucas, Meigs and Muskingum counties. You can perform a search on surname alone, without specifying the location if you are unsure.
http://userdb.rootsweb.ancestry.com/births

Ohio USGenWeb has some volunteer transcriptions of births online, searchable with the following link which requires javascript:
http://www.usgwarchives.net/search/search.cgi/searchoh.htm

If you wish to use other ways of searching by browsing or doing a search engine "site search", here is the URL for the USGenweb archives for Ohio:
http://www.usgwarchives.net/oh/

Find a Grave

This is a good website where you can look for information about locating an ancestor's grave. There are more than 53 million graves, often with pictures and headstone incriptions. You can search by name, by location, or by cemetery. Really good information here.

http://www.findagrave.com/

Ohio History

This is a fabulous indexed resource. I was only recently aware of the existance of the link which gives you access to so many articles and stories: http://publications.ohiohistory.org/. Here is an example from

GALLIPOLIS AS TRAVELERS SAW IT, 1792-1811

By JOHN FRANCIS MCDERMOTT

October 20, 1790.
An accident having happened to one of our boats, we have put into a small creek on the east side of this great river to repair the damages. I am now writing on the stump of a tree we have just cut down, so that you will not look for elegance or fine sentiment in this letter, which I send you by a young man, a native of Pennsylvania, who is going to New Jersey. We traveled by short days' journeys from the place of embarkation, and can not say much in favor of the manners of the inhabitants of the road by which we passed, a very few excepted, who paid some attention to us and sold the products of their farms at a reasonable rate; as to others, they took every mean advantage, and frequently imposed upon us, in a shameful manner, demanding three or four prices for the casual refreshments of which we and our little ones had occasion. We hope soon to arrive at our new territory, where we shall find things in their original state, such as God made them and not perverted by the ungrateful hand of man. To some the surrounding woods might appear frightful deserts; to me they are the paradise of nature; no hosts of greedy priests; no seas of blood to wade through; all is quiet, and the savages themselves shall soon be taught the art of cultivating the earth, refinement of manners, and the duties of genuine devotion. Under this free and enlightened dominion the unfortunate and oppressed of our nation shall ever find an asylum, our language and customs will here be preserved in their original purity for ages to come, and France shall find herself renovated in the Western World, without being disgraced by the frippery of kings or seeing the best blood wasted in gratyfing [sic] the ambition of knaves and sycophants. The weather is already cold, my hand is numbed, and our little temporary cabin is so full of smoke that I dare not venture in. So I bid you adieu.