Delaware is a small, historic state with a small, historic archives department. I'm happy to note that Delaware"s online archives are very neatly arranged in a series of collections.
The Archives Department has an unusual arrangement with Ancestry.com for free access to Ancestry's Delaware records. You need to have a state library card in order to make use of these freebies, however.
You can find a few more odds and ends at the Delaware Historical Society, although very little of their content is digitized.