New Hampshire State Archives hasn't discovered the scanner yet.
There really is nothing much here that's available online. Oh, a few assorted indexes and research guides are posted, but that's about it. No lookups. No photos. No nothing.
The New Hampshire State Library isn't much better, offering a collection of recent-vintage state publications (Treasury reports, budgets and the like)...what they call born-digital publications.
Over at the New Hampshire Historical Society, they offer a small handful of digitized photos, stereographs and postcards.
Lastly, there's the NH Vital Records website, which proudly notes that "Genealogical & Vital Records are not available online." They do have an online tool for statistical analysis of vital records, so I suppose that's something.
I couldn't even get a historical photo of New Hampshire from the state archives website, and had to swipe one from Flickr Commons. What a shame that a state with such a rich history has so little to offer in this internet age.
Update: All is not lost, it seems. Thanks to an alert visitor for pointing out NHDeeds, with links to the Register of Deeds databases in counties throughout New Hampshire. Each county has a different track record in terms of what's available, but you can generally search by family name for records of interest. Also have a looks at NH State Records, large downloadable files of state papers, including probates, back to the 1700s. Check the Index file for lists of names included in the records.