Fortunately if you are researching your early New Hampshire ancestors you have but a few places to look for probate records prior to the year 1800. Remember that New Hampshire, although de facto operating independently from the beginning, was legally administered by the Massachusetts Bay Colony until 1692. Afterwards it became the royal colony of New Hampshire up to 1776, when it declared its independence with the other colonies. In 1788 it became the ninth state to ratify the U.S. Constitution.
From 1635 to 1771:
The New Hampshire State Papers, a 40 volume set in print, includes all probate for the entire state in volumes 31 to 39. Only the major documents are given. For instance, it may tell you that an inventory appears and the date and amount, but not the content. For that you must look at the actual probate case files. Those are also filmed and part of the Rockingham County Probate records. Rockingham was the first county in New Hampshire and up to 1771, the only county. In addition to paper, these volumes are available in microfilm and in pdf format on a single CD.
Two other places should be searched for completeness:
Old Norfolk County Deeds, which included probate records as well. These records were abstracted in the Essex Antiquarian, which is available via Google Books or at the NEHGS web site [membership required].
Suffolk County, Massachusetts, which acted like a prerogative court for all of New England in the earliest time frame of 1630-1660. Wills and other materials were abstracted in the New England Historical & Genealogical Register in the 19th century. Genealogical Publishing Co. produced an 1984 book of these abstracts as Suffolk County Wills: Abstracts of the Earliest Wills Upon Record in the County of Suffolk, Massachusetts. The latest dates appear to be about 1670.
From 1771 to 1799:
At this point New Hampshire broke into three counties. Rockingham, Strafford, and Cheshire.
The Rockingham probate records are abstracted at: Helen F. Evans, Abstracts of the Probate Records of Rockingham County, N.H. 1771-1799, 2 vols. (Bowie, Md.: Heritage Books, 2000).
Helen F. Evans, Abstracts of the Probate Records of Strafford County, New Hampshire 1771-1799 (Bowie, Md.: Heritage Books, 1983).
Cheshire County--no abstracts have been done to date.
Naturally all the original records have been microfilmed and are available in a number of depositories.