Here in Georgia, our virtual library is called GALILEO, and though I might be a little bit prejudiced, I think it's fabulous. Georgia residents get a password from their public library, and then they can log into hundreds of resources: full-text articles from journals, magazines, and newspapers; digital displays from state archives; government documents; reproductions of historic diaries and newspapers; online encyclopedias, dictionaries, and other reference books.
GALILEO even provides a number of databases--plus the Digital Library of Georgia--that guests can use.
Most states today have some kind of online, virtual library for their citizens. I'm trying to search them all out for you and provide a listing of links on my research wiki: Facts for Fiction. I'm finding that the resources as well as the policies for accessing them vary widely from state to state. So you'll just have to check out the ones that interest you and see what they have.
Here are the states I have so far:
I will keep adding states to the list, and I'll keep you (and Facts for Fiction) updated.
If you have information to add about your state, please let me know.