The FamilySearch site now offers a searchable name index to New Hampshire birth records from 1640 to 1900.
Don’t get too excited yet. Official NH birth records were created by town or city clerks. In 1866, New Hampshire passed a law requiring towns and cities to send copies of birth records to the state. However, some towns and cities didn’t comply until the 1880s, so less than half of the population has birth records at the state level. This online index is from the handwritten card index at the state level. If you don't find what you're looking for, remember that New Hampshire towns and cities have more births recorded than what's available on this statewide card index.
The cards may include child’s name, date and place of birth, name of parents and their place of birth, occupation and ages of parents, name of attending physician or midwife, gender, color or race, living or stillborn, and place recorded. With this information, you will be able to order the original record from the birthplace or state.
For example, the FamilySearch index lists Martha (b. 1654), Ann (b. 1658), and Nathaniel (b. 1660), children of John Huggins (1609-1670) and his wife Bridget (d. 1695) of Hampton, NH. When you click on the individual names, you can view the transcription and the card image. These three cards were created in 1906, and list only child’s name, parents’ names, birth date and place, clerk’s name (transcriber) and creation date.
John and Bridget Huggins, however, had nine known children. Besides the three listed above, two more births and one baptism are listed in Vital Records of Hampton, New Hampshire to the End of the Year 1900, Volume 1, by George Freeman Sanborn and Melinde Lutz Sanborn.